A draw call is a function used by a program to instruct the GPU to draw something. In games this is done once per frame, normally lots and lots of draw calls per frame (sort-of roughly analogous to your monitors refresh rate). In general you have one draw call per texture file used per object, but it may be more than that if you specify particular material types, ahh, check that, let's call it "qualities" so we SU folks are clear it's something different from SU materials, to influence the appearance of the texture. Such "qualities" might be gloss, brightness, various types of finish, like metal, rubber, wood, etc., and then whether there is an alpha channel present of not (transparency)
So given one model, 4 texture files, 2 of which have an area of transparency, 3 of which have areas where those "qualities" apply, the draw calls would be 4 for the four texture file as applied to a basic appearance, 2 for the transparencies, 3 for the "qualities, for a total of 9 drawcalls. For a game, that's 9 per frame for the one model. In a complex game there might be a couple of hundred models in view so that may add up to several hundred or even a couple of thousand draw calls, depending on complexity.
Because there is hardware involved each draw call is a CPU interrupt -- hello, this is long distance from America for Mr. Floyd... is Mr. Floyd there?.
In addition to letting the GPU know it is supposed to do something, a game will also provide the mesh for each object that is to be drawn, which is all of the xyz data that forms the vertexes of the model as well as the UV mesh which tells the GPU how to align the artwork. For each model for each frame.
In my experience it starts to get hard to keep frame rate equal to or above the monitor refresh rate when the draw call count exceeded 500 per frame.
On the front side of the glass sits the game player, who, quite naturally, does not want to see any slow-downs/speed ups. The net effect is to place a burden on model builders and artists to make their stuff so it requires the fewest draw calls possible. SU is not particularly good at this but at least has the benefit that things can be done very quickly and so it can have a proper place for both prototyping ideas and doing fairly basic game models.