Learn Spanish (Spain): El tablero está sobre la mesa.

We use estar because we are talking about physical location. A good rule to remember is that estar is always used to say where physical objects or people are located, even if they never move. We use ser for defining characteristics, identity, or to say where an event takes place.

Could I say en la mesa instead of sobre la mesa?

Yes, absolutely! The word en is very common and can mean either 'in' or 'on'. However, sobre specifically means 'on' or 'on top of'. Using sobre removes any ambiguity, though with a table, en la mesa is usually understood perfectly well as being on top of it.

Are there other common meanings for the word sobre?

Yes! Besides meaning 'on' or 'over' for physical location, sobre can also mean 'about' when discussing a topic. For example, you might read a book sobre historia (about history). It can also mean 'envelope' when used as a noun (el sobre).