What is the real meaning of the phrase 'You're either part of the solution or you're part of the problem'?

Basically, there are two sides to an issue or a conflict (the Pros and the Cons). As an individual, you lie on either one side of the situation or the other. This means that if you are making an actual or physical part or effort in resolving the problem or situation, i.e., making actions and genuine effort to either recruiting others to aid in the resolution, or accomplishing deeds or tasks that efficiently and successfly remove obstacles standing in the way of the resolution, and/or making successful accomplishments or tasks that solve or complete or finalilze the resolution to the issue or conflict, then obviously "you are part of the solution".

Otherwise, you lie on the other side of the fence, "being part of the problem". Keep in mind that even if you are not making any physical efforts towards making the problem worse, perhaps not doing anything at all, or turning your cheek to the issue, is still "being part of the problem".