What is the Significance of Constraints in Relationships Between Variables?

[Astrum]

I have no idea what constraints are, nor do I understand why they are important.

I get where the constraints in these two examples come from, but not why they're significant.

These seem to be relationships between variables, and not much of a "constraint" in the sense I know the word.

Can someone give a quick definition or some insight into this?

 

[Simon Bridge]

I have no idea what constraints are, nor do I understand why they are important.

If I chained you to a wall - the length of the chain is a constraint on your motion. The size of the wall is another one.
I'm pretty sure you would be able to tell why these constraints were important.

I get where the constraints in these two examples come from, but not why they're significant.

There are quite a few - you understand why the wedge being constrained to move only horizontally is significant right?

So which ones do you have trouble with?