One thing to keep in mind is that people on shows like that often use linguistic shortcuts. Rather than saying something like, textural variation---which is what they most often mean (see, for instance, the examples given above), they just say "texture." Which can be, understandably, confusing.
"Texture" refers to the consistency of the dish or ingredient being discussed. So, to put a point on it, creaminess actually is a texture. But, used alone, it could be boring. So we vary that texture with another one, perhaps adding some "crunch," or some "grittyness," or some "tooth," etc.
Texture is indirectly related to flavor, because we often interpret taste based on the mouth feel. For instance, let's start by making a butternut & apple soup, with the main ingredients diced and cooked to the tender-crisp stage. Now take half of that soup and puree it. Try them side-by-side and they will taste different, even though the ingredients are exactly the same. Maybe you like the pureed soup, but find it a little cloying. So you add a textural break; possibly sprinkling it with roasted pumpkin seeds or crumbled bacon.
On the shows you've been watching, they'd say you used the pumpkin seeds or crumbled bacon to add texture. But what they really mean is that you gave your mouth a break from the uniform texturee of the puree.