Something that "builds up" becomes stronger or thicker over time by gradually adding more and more. For example:

No one cleans over there, so the grease just keeps building up.

You have to gradually build up a base of clients.

In the example above, the speaker wants to explain that crud gradually becomes thicker and thicker inside the car's engine.

Some other things that also "build up" include:

• build up your confidence
• build up military forces
• build up tension (in a movie, book, or TV show)