What's the name of the "circle" that the arrow points to?
In the picture is the end of a barbell. That thing that arrow points to is put onto the tube. The tube has a "dent" where that circle fits. There are eyes in the end of the circle that are used to expand it slightly so it can move easily onto the tube and when it's in the dent, it's released so it clasps.
The clips that you are referring to are called snap rings in North America.
That is called a "circlip" and can be removed or positioned with special pliers made for them. They come in internal and external varieties. What you have pictured are internal. Some circlip pliers are reversible (the ones in the picture) so you can use them with internal or external circlips.
I've also seen them called C-Rings* or C-Clips, to differentiate them from E-Clips/E-Rings. E-Clips perform a similar function but have a slightly different shape, including a spacer (the bar in the middle of the "E") which keeps the ring at a set distance from the shaft:
*If you Google "C-Ring", add the word "retaining" or have Safe Search on!
