A more practical difference between Block and Module can be seen here:
Module[{x}, x]
Block[{x}, x]
(*
-> x$1979
x
*)
So if you wish to return eg x, you can use Block. For instance,
Plot[D[Sin[x], x], {x, 0, 10}]
does not work; to make it work, one could use
Plot[Block[{x}, D[Sin[x], x]], {x, 0, 10}]
(of course this is not ideal, it is simply an example).
Another use is something like Block[{$RecursionLimit = 1000},...], which temporarily changes $RecursionLimit (Module would not have worked as it renames $RecursionLimit).
One can also use Block to block evaluation of something, eg
Block[{Sin}, Sin[.5]] // Trace
(*
-> {Block[{Sin},Sin[0.5]],Sin[0.5],0.479426}
*)
ie, it returns Sin[0.5] which is only evaluated after the Block has finished executing. This is because Sin inside the Block is just a symbol, rather than the sine function. You could even do something like
Block[{Sin = Cos[#/4] &}, Sin[Pi]]
(*
-> 1/Sqrt[2]
*)
(use Trace to see how it works). So you can use Block to locally redefine built-in functions, too:
Block[{Plus = Times}, 3 + 2]
(*
-> 6
*)