Besides the meaning of "having" or "acquiring" something, "get" also can be used to mean a process is happening, as in your example. "It is getting colder every day" means the weather is becoming colder with each passing day.
Another slang meaning is given in the following example:
"Do you understand?"
"Yeah, I get it!" / "No, I don't get it!"
Both mean "understand" in this example.
I will stop here since there are many usages of "get," but if you have specific examples, please write them out.