ChessBase is not available for Mac but there are some alternatives that runs on macOS with similar functionality. The best Mac alternative is Scid vs. PC, which is both free and Open Source. If that doesn't suit you, our users have ranked more than 10 alternatives to ChessBase and five of them are available for Mac so hopefully you can find a suitable replacement. Other interesting Mac alternatives to ChessBase are ChessX (Free, Open Source), ChessDB (Free, Open Source), Chess Insight (Paid) and Scid on the go (Free, Open Source).
Shane's Chess Information Database is a powerful Chess Toolkit, with which one can create huge chess databases, run engine analysis, or play casual games against the computer or online with the Free Internet Chess Server.