I've already covered some of this on my web site under Curly Hair Basics, but I'm going to expand on it here.
Hair texture is the thickness or diameter of the individual hair strand. Your hair texture plays one of the most important roles in how you should care for your curls, not only through daily maintenance, but also when considering any chemical services such as haircolor or texturizing. Even how your hair is cut needs to be adapted to the texture of your hair.
There are three different textures: fine, medium and coarse. Not everyone has the same uniform texture over their entire head, however; for example, you can be fine at the nape and coarse at the hairline (especially if those pesky grays are starting to pop up). The hair textures are:
Fine hair can appear very limp or flyaway and does not hold a style well. It frequently seems dry, when in fact it is quite often over-moisturized. It is very easy to over-process and is quickly damaged by chemical services if great care is not taken. Products with a lot of humectants and emollients should be avoided in favor of those with protein.
Medium hair is what is considered “normal” hair, meaning it has a mid-range texture. It does not require any special considerations for chemical services and usually processes normally. Undamaged hair with a medium texture can generally support products with a wide range of ingredients.
Coarse hair is much thicker and stronger than fine or medium hair, but typically does not bend and cannot hold a style well. It is also often dry and brittle, due to an overabundance of protein. Coarse hair is much harder to process and is often very resistant to chemical services. Products with a lot of protein should be avoided in favor of those with humectants and emollients.
Hair texture is key to establishing the best routine for your hair. As I've said before on many other occasions, those popular "curl classification systems" that help you in identifying your wave pattern from a visual perspective are absolutely useless when it comes to caring for your curls. Let's say you and I have the same exact visual spiral pattern, so we both consider ourselves "3b." And let's say we both have about the same thickness of hair (density) but my hair is fine and yours is coarse. Those curl classification systems would still lead us to believe we have the same hair type because we are visually almost identical, right?
However ... if we try to use the same products because our hair "looks" the same, guess what is going to happen? If we are using products with heavy proteins, my hair is going to look fabulous and yours is going to look like frizzy, crackly dry straw. If we use products with heavy emollients and humectants, your hair will look like a million bucks and I'll have a flat, limp mess. You cannot look to those visual classification systems for information on how to properly care for your curly hair. Only your hair properties -- texture, porosity, density and elasticity -- can tell you that.
Here's another interesting tidbit for you: did you know that different hair texture types respond differently to the kind of cutting they receive as well? For example, fine hair needs to have a cut with more weight because it tends to lie flat no matter how short it is. Short cuts can be problematic for coarse hair that is very thick because hair with a coarse texture expands naturally in an east-west direction. Even with a curly dry cut, the methodology remains the same, but the stylist has to take all kinds of other factors, including your hair texture, into consideration.
There are special considerations with color as well. The melanin (color pigments) contained within your hair shaft are grouped more tightly in fine hair, so color takes faster and can look darker than expected (because less light is able to reflect through those tightly packed color molecules). With coarse hair, the hair strand has a larger diameter and the melanin pigment is not so tightly packed, so it can take longer to process and can look a bit lighter.
Other than porosity, I would call hair texture the most important hair property there is. Your curly hair care routine will hugely improve when you start taking your hair texture into consideration.