"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.