You make an advance when you try to meet someone and make their acquaintance. It is usually used when a man tries to make the acquaintance of a woman for romantic reasons. However, it is used in other instances. One nation can make advances to another nation for a peace treaty, for example. In that case, the nation could also 'make overtures' to another.

My boss thought I was making advances but I was just interested in the project. My boss though I was putting the moves on him but I was just interested in the project. My boss thought I was romantically interested in him but I was just interested in the project.