Welcome to Sudbury my friends. Houses here are often built on bedrock, and it’s not terribly uncommon to see some of that bedrock poking out in the basement. With that bedrock almost always comes a trickle or two of water (it’s near impossible to seal a foundation around a non-uniform piece of bedrock)
First, it’s totally normal, and ok to have, but it may require a little extra attention to ensure things don’t get out of hand. We’ve spoken to many home inspectors and foundation professionals over the years. There are simple solutions to help make the space livable and a non-issue.