"Getting __" means "becoming ___".

You use this phrase to talk about a process that started in the past, has a certain goal or end point, but hasn't finished yet.

For example, when you sit on the ground for a long time, your back will eventually get very stiff. When you ask someone:

Is your back getting stiff?

...you're asking whether they are starting to have a stiff back. You're assuming that their back wasn't already stiff at the beginning.

Some other examples:

I'm getting tired.

It gets a lot easier if you stick with it.