What does the term legacy database mean?

legacy: anything from the past that keeps coming around to haunt you.

A legacy database is generally something that you will have to inherit and base some of your design decisions around. Most companies that put out work may already have some other (usually horrible) solution and you need to give them a bigger and better product...

BUT

It has to work with all of their old legacy data. The company is not going to want to manage two different applications just so they can keep all their old records. You will need to develop your solution to be able to migrate the data from the legacy system over into your system. This can have a massive impact on the overall design of the new database, because it cannot stray too far from the previous without introducing a lot of problems in terms of data integrity.

In the general context, it can refer to any of the older database technologies.

In a more specific context, it can refer to a database system that was inherited by a team from previous project owners.