Great question about the mantle!
You should think of most of the mantle as consisting of a very thick liquid—like cold honey in terms of its runniness, not its temperature. On top of that honey-like mantle floats the rigid crust and the brittle uppermost part of the mantle (which together form the plates of plate tectonics).

Well…the deeper in Earth we go, the hotter it gets. So, Earth’s core, is its hottest part. The core is like a flame on a stove, heating the stuff above it, only the core heats 360 degrees in three dimensions, since “above” is all directions away from the core.

Most substances expand (and become less dense) when they get warmer, causing that warm material to rise. (Water is weird. Cooling it forms ice, which floats (!), because it’s LESS dense than liquid water—but that’s a different story). The base of the mantle, sitting near the hot core, warms up, and begins to rise very slowly (since the mantle’s very thick—viscous is the word scientists use). As the mantle moves upward, it encounters cooler and cooler temperatures, causing it to become denser, and ultimately sink. After sinking, it heats up again, and then (you guessed it) rises again. This cycle of rising and falling sets up big currents in the mantle (called convection cells). These slow currents are one of the things that push plates around, causing, among other things, continental drift.

Water convects in a boiling pot of water for the same reason that the mantle convects, its density changes as it alternately cools and warms (only when liquid water turns to a solid, does water act oddly—that is, it becomes less dense).

Although you probably don’t drink coffee (which is the best for your health), it’s a wonderful way to learn about convection. After pouring yourself a hot cup (a clear cup, or measuring cup works especially well), let it sit for a minute. Then add a couple of tablespoons of milk from the bottle or a pitcher. At first, the cold milk sinks to the bottom of the cup, and most of the coffee at the top of the cup remains black. The milk sinks because it’s colder and denser than the coffee. A second or two later, however, after the milk is warmed by the coffee, it wells upward, and soon all the coffee and milk in the cup become mixed, even without stirring. Convection has done all the work. A marshmallow floating on that coffee would be pushed around by those convection cells, the same way that the crust is shoved around as it floats on the convecting mantle.

Imagine what happens when you boil water on the stove. You heat the water from below, and the hot water from below rises to the top, whereas the cool water from above sinks to the bottom. See image. We call this convection. Why does the water move? The reason is that hot water is less “dense” than cold water, and anything less dense than the surrounding will float upward.

The same thing happens with hot air that rises above cold air. This convection is the reason why a hot air balloon flies. On the Earth, you have a similar situation than in a hot stove. The center of the Earth is hot, and the surface of the Earth is relatively cool. Therefore, the mantle that is heated from below will rise very slowly to the surface, and the cool mantle at the surface will sink. This convection in the mantle affects the rigid crust of the Earth and drives the movement of the plates on Earth’s surface. image here.

Great question! Imagine taking something thick and gooey like a bowl of pudding and placing something light and solid like a graham cracker on top. If you jiggle the cup of pudding, the graham cracker on top is going shake back and forth. In this example, the pudding is the mantle and the graham cracker is the crust.

In the Earth, we can think of the crust as "floating" on top of the mantle, like how the cracker floats on the pudding. Because the pudding (mantle) is less rigid it can flow more easily, and when it flows the graham cracker (crust) floating on top will move with it.

One important thing to remember though is that the Earth's mantle is not liquid like magma! It is made of hot, solid rock. Because the rock is so hot, it can flow like the pudding. The mantle moves because of something called convection.

Convection is basically the way the Earth cools itself off by moving heat from the inside of the Earth to the outside. As hot rock rises up from the deep Earth, it carries heat with it. That heat comes through the crust through volcanoes and rocks in the crust. Then when the mantle rock cools off, it falls back down towards the center.

This pattern of convection is what causes the hot mantle rock to flow and carry the floating crust on top!

The mantle allows the crust to move and also, in a way, drives the motion of the tectonic plates. The mantle is more or less solid rock, but the high temperatures (>1000°C / 1832°F) and forces present far below Earth's surface can deform the mantle, albeit slowly. The mechanism for motion of tectonic plates is still an open question. Early in the development of the theory of plate tectonics, convection currents in the mantle were thought to push and carry plates. In this process, hot material from near the core of the earth would rise (due to lower density, like convection of hot/cold air ). To make room, the cooler mantle rock above it would be pushed sideways. Because the cooler rock is in contact with the plates, some of that sideways force would be transferred to the plates, and they would also move. However, modern research has found several inconsistencies with this theory.

First, convection cells large enough to drive motion of the plates have not been found, and the material between the mantle and the plates is weak enough that the forces transferred from the convecting mantle to the plates is small. Further, measurements indicate that there are multiple convection cells beneath plates. This is problematic because they would not push plates in the same direction; their effects would counteract each other and hinder plate motion.

The modern theory is that gravity drives plate motion through two processes called "ridge push" and "slab pull". Convection in the mantle still plays an important role though. The hot rock in the mantle rises and pushes up mid-oceanic ridges at boundaries between plates. At these ridges, the plates are essentially on top of a hill.

Analogously to an avalanche, gravity pulls the plates downward. As the plates slide down the slope of the mid-ocean ridge, they push adjacent plate material away from the ridge. This is the "ridge push" process. At other plate boundaries (namely, subduction zones), one plate is driven below another. The sinking plate is more dense than the surrounding rock, so the gravitational force on it is stronger. As the plate sinks, it pulls the material behind it farther down as well. This is the "slab pull" process.

Another effect of the mantle in this theory is to prevent motion, essentially through friction against the moving plates.

While this second set of mechanisms is the current theory, movement of the crust is still undecided and a matter of much debate and current research.

[References: Incorporated Research Institutions for Seismology , including the video on the right side of the page; Geological Society; and Columbia University .]

It's complicated, but interesting. The crust is sitting on top of the mantle, but is attached to the top of the mantle because the mantle is an extremely viscous fluid (it's so viscous that we would normally call it a solid, not a liquid. It's far more viscous than glacier ice, for example).

Ocean crust is dense and so sinks, and pulls the mantle along with it. Continental crust is less dense and so floats, but because it's attached to the mantle underneath it, wherever the mantle moves, the continents have to go with it. Finally, hot plumes of mantle rock coming up from the core or just deeper into the mantle force the cooler mantle that they're moving through away, which also causes continents to move.