What happens when I tap the map?

The visual effect is what we refer to in the industry as "feedback". It is a way of confirming input, where other elements in play may not.

If you tap on an object such as a pokémon or a pokéstop, and you see that effect, it means that the game has not registered your input on an object. Instead, it has interpreted your tap as being on vacant ground.

Apart from that, the effect has no other function.

Actually, there is an effect: in case you have only one hand available, you can zoom by tapping the map and then dragging downwards from the blue circle that appears.

But that is its only function.