You mean the white spindle with the blue thread on it?

It's called a bobbin. It's fixed in place. The whole thing is held in place and all the thread comes in from the side (face).

The only way I can think of it right now to describe it is it's like looking at a skee-ball machine. If you drew a 2-D picture, it would look like 3 concentric rings so nothing can get to the center. But it's not 2-D, it's a cross section, and much like a ball can enter from the third dimension, the thread can too.

The bobbin is on a horizontal shaft, with a vertical face facing where the needle will pop down. When the needle pops down, a little whirling finger catches the thread and loops it around the bobbin once, then lets it go and it is snatched back up out by the needle.