1. To continue making progress (in some endeavor) at steady, consistent pace, especially in the face of difficulties, challenges, setbacks, etc. We're still plugging along with the project, in spite of all the problems we've had with staff turnover. It's been tough dealing with all the negative publicity in the media, but I just want to plug along and show the world that I can still win this tournament.

2. To get by; to do satisfactorily. Typically used in the continuous tense as a response to "How are you?" or some similar greeting. A: "How you been, Tom?" B: "Oh, you know, just plugging along. Nothing too wild going on around here."