What does it mean?

People bump because it will bring the topic back to the top (so more people can look at it). The older posts always get pushed to the bottom by newer posts.

Some people say it stands for "Bring Up My Post". The original poster ("OP") might use it so that more people will see their post and maybe reply. Other people can use it to mark a thread they want to follow as they can then find threads they're interested in easily under "My Topics" above.