Energetically start doing something, as in Come on, let's swing into action before the others arrive. This idiom uses swing in the sense of “move vigorously.”

What does to swing into action mean?

: to quickly start doing something They have to be ready to swing into action at a moment's notice.

What does it mean to swing by something?

US, informal. : to make a brief visit I'll swing by after work to drop off the paperwork.