These fish have eggs inside them. If they are fertilised they grow and the fish gives birth (or spawns) to fry.
If they do not get fertilised then nothing happens. Like humans, we have eggs inside us too but nothing happens if they don't get fertilised.
You will know if the fish has been fertilised as she will get fatter and fatter.
A tank with lots of fine leaved plants for the newborn fry to hide in is required as most livebearers are also happy to eat the fry as fast as they are born. What they miss, the other inhabitants go for.
Livebearers not only don't need the male kept with them, they then don't need the male for the next 3 - 4 months as they can store the sperm and produce then next 3 or 4 batches on their own.
To get livebearers to breed you need 1 male to 2 or more females and leave them to it. They will know what to do 8)
Depending on temperature, livebearers will produce new babies (spawn) every 4 - 6 weeks.