When i should use it?

For example when you would like to animate an object squishing through a choke point in a pipe.

Check this video out:

All I did was to add a lattice modifier to the iso sphere and animate it going down through said lattice. That's it.

Just imagine the pain of animating the deformation by hand. And this solution is super flexible. I can make it bigger, change the size of the individual segments, I could even make the lattice follow a curve. 

This is of course only one example of when to use it.