To "get around to" doing something means to finally do it after a long time. You can use this phrase when someone is busy:
Just check this over and send me your response whenever you can get around to it. Thanks!
Or you can use "get around to ___ing" when you don't think someone is busy, but just that they're being lazy. This is the way that it was used in the example at top. For another example, a mother might say to her son who's in college and living in the dorms:
Oh, so you finally got around to calling me, huh?
The meaning of this message is "I'm upset that you didn't call me sooner."