Good question! It turns out there are three different ways that heat can be transfered. The one you might be most familiar with is conduction: this is what happens when something warm and something cold touch and heat passes from the warm object to the cold object directly (for example, if you touch something hot or cold, this is how your hand is able to sense it).

Second, there's convection: in convection, heat is exchanged by physically mixing two fluids of different temperatures. For example, if you put some cold milk into some hot tea or coffee, the milk warms up and the coffee cools down as the two liquids mix together.

Finally, there's radiation. This one's a bit more complicated, but the basic idea is that every object is constantly radiating away energy; this is because all objects are made up of atoms that are constantly jittering around. These atoms are made up of electrically charged particles, and these particles emit electric fields. As they jitter around, these electric fields jitter as well, and can turn into electromagnetic radiation (this is actually what makes up the light you see - it's just waves in the electromagnetic field! And that's why when an object gets really hot, it starts to glow red - its atoms jitter faster and faster until they emit light). But just as the jittering of atoms in objects causes them to emit electromagnetic waves, so too can electromagnetic waves hitting an object cause its atoms to vibrate faster, increasing its temperature. For example, the red glow you see coming from coals in a fire is a form of this electromagnetic radiation, mostly in the form of what's called infrared radiation. When you hold your hands up to a fire, the heat you feel comes from the infrared radiation hitting your hands and making the atoms in your hands vibrate faster.

Exactly the same thing happens with the sun and the earth: the surface of the sun is very hot and is constantly emitting electromagnetic radiation (including light and infrared radiation). These electromagnetic waves don't need a medium to travel through, so they can just travel through space from the sun to the earth, and when they hit the surface of the earth, they heat it up. That's why the sun feels warm on your skin! Its infrared radiation is the same as the infrared radiation you feel coming from a fire.