I'm not sure I understand what you're asking for... Are you wondering if there is an application of this ?

I can show you one (the first that came in my mind), but it has to do with measure theory (product sigma-algebra). So if you're interested, I can show it...

And Opalg once used them to explain stuff in product topology.

There another way of seeing these functions, it's calling them the coordinates mappings :

$\displaystyle \pi_1 ~:~ A \times B \to A$ (note that it's $\displaystyle \to$ and not $\displaystyle \mapsto$, I don't know how you learnt it, but my teachers always used the second one for defining the function)

$\displaystyle (x_1,x_2) \mapsto x_1$

$\displaystyle \pi_2 ~:~ A \times B \to B$

$\displaystyle (x_1,x_2) \mapsto x_2$