Excellent question!
The coldness that you feel when you are outside on a winter day is from your body and the outside air trying to become the same temperature. You lose body heat trying to warm up the environment-- since there's much more of it than there is of you. Heat "travels" in a few different ways: conduction, convection, and radiation. For a fabric or jacket to be insulating, you want to slow down the transfer of your body heat to the environment.

The first method is to have a fabric that is very thick or has a lot of loft. A good example is fleece. Fleece is a fabric that is knit and then brushed so that it almost looks like fur. The fur "pile" traps still air, and the thicker the fleece, the more difficult it is for heat to escape. Thicker does not necessarily mean heavier though, you can have a thick fabric that weighs the same as a thin fabric. This is why fleeces became so popular because their loft is usually very good for their weight. We are slowing down conduction in this case because it's hard for heat to move through a thicker barrier.

However, most fleeces let wind come right through. Moving air feels cold because it moves heat away via convection. For this, we can use a fabric with low air permeability to feel warmer. An example of this is a "windbreaker" or any rain jacket. These fabrics let less wind come through because they are woven tightly (have less spaces/holes in the fabric) or have a waterproof coating (think of it like a plastic bag "film" attached to the fabric). The downside is that if you are sweating a lot, these types of jackets can feel clammy because your sweat can't evaporate through the fabric to keep you comfortable-- this steam-room effect can actually chill you in the same way a light breeze cools you off more when you're sweating and exercising than when you're already dry and comfortable.

The last way we can insulate is preventing heat loss via radiation. Emergency blankets are metallic looking because they reflect infrared radiation coming from your body back to you. Infrared radiation is the same thing that makes sunlight on your skin feel warm, although the sun emits a lot more infrared radiation than a human body. Why aren't there metallic-fabric jackets? Well, we're starting to see some, but most metallic-looking fabrics are loud, crunchy, and uncomfortable since they "breathe" worse than windbreaker/rain jacket-type fabric. The tradeoff isn't worth it for most people and climates.

So to summarize, different types of fabrics insulate better because they slow down your body heat from escaping via conduction/convection/radiation. Some are thicker, some are more windproof because their structure lets less air through, and some can be reflective to bounce infrared radiation back to your body.

Usually, you need to use multiple fabrics to accomplish this, so bundle up by layering! My go-to system is either wearing a fleece underneath a rain shell, or a down jacket where you have tightly woven fabric sandwiching incredibly lofty goose down/feathers. Just don't over-do it to the point where you get too hot and sweat =)

(please note the opinions and facts shared above are that of the individual and do not represent those of The North Face)

There is a property of a material called "thermal effusivity," that basically describes how easily the material loses heat to the environment, and how much heat it holds in general. So, it combines the ideas of heat capacity (which is how much head a material can hold) and thermal diffusivity (how quickly it gives away the heat). Whether this property is low or high depends on many factors. There is the chemical part (what compounds and molecules the materials is made of) but also a physical structure and packing part (for example, down feathers hold a lot of heat, due to their structure, or, clothing with layers keeps in more heat).

By looking at the chemical makeup of the clothing and the physical structure of it, you can determine how well it will insulate.

Fabric insulates by trapping air between it and within it. Air that isn't moving can still transfer heat by conduction, but not by convection, which is the most effective method of moving heat.

So the key concept which you probably already understand is that when you have something hot next to something colder, heat flows from the hot object to the colder object. This process is called heat transfer and is unavoidable, but by using insulation, the rate of heat transfer can be reduced. Heat transfer happens by molecules colliding with each other which transfers some energy. Some materials don’t transfer as much energy when molecules collide into them. These materials are called insulators and are important in a lot of different places. For instance, there is insulation in the walls of your house so that when it’s a cold day, your house doesn’t get cold. In general, the substances that transfer heat the fastest are solids, followed by liquids, then gases. An interesting application of insulators is if you wear a jacket when it is cold out. The jacket doesn’t actually provide any heat the way a radiator does, but what it does do is that is slows down the rate at which heat leaves your body into the air.