Since you said "Terminator movie s", Keen's Causal loop answer cannot help you. But fortunately there are two other answers around, which greatly explain how the Multiverse Theory explains things (though watching a bit of doctor-who won't harm your understanding, either). It boils down to multiple timelines existing, and each time travel spinning a new one off. There are many timelines in the Terminator universe:
0: The "original" timeline: No one came from the future, which obviously means John Connor's father was not Kyle Reese, but probably still a soldier who soon fell in a conflict (in order to be consistent with what this future's John Connor told Kyle§), which probably traumatized Sarah enough to bring up John the way she apparently did. The future as described by Kyle in the first movie happens.
1a: An short-living timeline, in which only the Terminator went back in time, effortlessly killed all Sarah Connors%.
1b: Kyle Reese followed the Terminator, saved Sarah and wiped
1a from existence - not without doing the nasty in the pasty and becoming John Connor's father. End of the first movie. Sarah raised this John probably even more prepared for the unpleasant future, but overdid it (by attempting to blow up a computer factory, the name of which was not revealed) and ended up in a psychiatric clinic (whether that also happened in
0 is not known).&
2a: Once again, only Skynet's Terminator travels back and therefore (probably) succeeds in killing the young John Connor with results similar to
1a (though you probably shouldn't underestimate this timeline's Sarah Connor).
2b: And once again, John Connor's soldier, this time a Terminator, too, travels back and saves the day. Since this Terminator told Sarah about Cyberdyne's involvement in
1b's future, the future was influenced much more severely by blowing the facility up and by making sure Miles Dyson didn't research Cybernetics any more (his death wasn't necessary for this though, his survival might even have helped preventing the post-T2-Skynets from happening). The future seems uncertain*, and as the third movie confirms, the Skynet-related events of 1997 didn't happen. Of course, as the third movie also shows, a different, decentralised, Skynet arises in 2004, suggesting the effort was not entirely in vain but rather delayed Skynet's arrival at the price of making it more difficult to wipe out. This future's John Connor got fooled by an Arnie-Terminator and Skynet considers his future kids with Kate, and thus the present's Kate, the more worthy target for YATSBIT (Yet another Terminator sent back in time). I only bothered to watch this movie once and can't remember whether this Skynet was also close to losing or simply wanted to self-improve its past.
3a: Yet another lonely Terminatrix, killing Kate (and afterwards probably John, while she's at it), once again in a timeline that seems to vanish with
3b: Once again, John Connor's soldier (see where this is heading?) saves the day. Well, kind of. He didn't assist in (nor was he ordered to) preventing Skynet's emergence, but he was also quite busy...
Barely remembering the fourth movie (which didn't involve time travel, though) and not yet having watched The Sarah Connor Chronicles (which apparently introduces yet another timeline
3c) there might be additional timelines to mention.
§ Feel free to speculate it even was a relative of Kyle. Skynet was (or, will have been, whatever, I'll stick to past tense) created, its creator remains unknown since Kyle never told Sarah.
% You may speculate what he did afterwards (e.g. deactivate, go into hiding, help developing an advanced Skynet to start with), but it doesn't matter since nothing prevented this timelines immediate termination via
1b. Maybe this future with a happily undefeated Skynet exists in parallel, maybe it failed otherwise...
& Maybe she managed to escape or "recover", maybe she didn't, anyway the second movie's original future happens, which doesn't seem to differ much from the
0-future+ apart from the first Terminator's leftovers being used to probably create a better Skynet to start with, or maybe Cyberdyne systems was a competitor to
0's Skynet-creator and now had a head-start yet ended up with the very same Syknet.
+ Though I wonder whether the first movie's time travels did actually occur here - it doesn't seem necessary, though it would stabilize
1b into a potentially closed causal loop
2b seems like an unstable timeline, unless Skynet and John sent back "their" Terminators from this future despite knowing about the result, i.e. basically only to close the causal loop.