When you serve, you have to get the ball into the service court diagonally opposite you, yes? Obviously your first attempt at that is your first service, and if you hit it straight into the net, or get it over the net but it goes too long or wide, that counts as a fault and you get another go, which is your second service. (There's also occasionally foot faults, but I'm not entirely sure of the rules around those). If that also goes into the net, or long or wide, then that's a double fault and you lose the point.
However if your first attempt clips the net on the way over, but still lands in the service court, it counts as a let, not a fault, so the umpire says "let, first service" and you are still counted as being on your first service. You can have several lets in succession and still be on your first service, and not lose the point. If you then serve long/wide/into the net or the ball clips the net and goes long or wide, you're then on your second service, and at risk of losing the point. If at that stage your serve clips the net but lands in again, you've got another let, but this time the umpire will say "let, second service" to indicate that you've not yet lost the point and can serve again. As with your first serve, you can serve several lets on your second serve, and the umpire will say "let, second service" each time. But to be honest, if you're clipping the net that often on your serve, the odds are it's going to ping wide or long at some stage and you'll lose the point.