In pure functional languages, functions are not 'invoked', rather a set of arguments is 'applied' to them. Now, if all the arguments are not passed in, then the function is being 'partially' applied. Partial application converts variadic functions (i.e. functions with multiple parameters) into functions of lesser arity by pre-specifying certain argument values.
The biggest advantage of using tail calls is that they allow you to do extensive operations without exceeding the call stack. This makes it possible to do a lot of work in constant space without running into out of memory exceptions; this happens because the frame for the currently executing function is re-used by the newly-executed function call.