As to credentials: for two years I built the majority of levels for the forthcoming single player FPS title Darkest of Days. Anything written here is backed by my own experience and observation from building and playtesting.
The sawtooth is such a universal staple of level design that once sensitized to, you will notice them everywhere. It is simple, effective, and (generally) foolproof.
The sawtooth stops the player from going backward. Simple as that. But as with other central design tenets of level design, simple can have far reaching connotations.
It takes innumerable shapes and forms: a broken staircase, a drop-down, a chute, a sheared cliff. Some are obvious, some are seamlessly integrated into the environment in a natural way, some are completely blind--like a ventilation duct that drops out from under you (groan).
Careful modulation of both the obviousness of sawteeth and their frequency are critical to the player's immersion. And the more "realistic" a game purports to be, the more carefully masked and generally less frequent they'll need to be to not be disruptive.
But why impede backward travel in a level? For single player games, there are a number of reasons: it makes life easier for the designer and the for the player in several ways.
The designer no longer has to worry about whatever the player is doing--getting lost, wondering where the party is, getting bored, and eventually quitting (which is the worst thing that can happen for a designer).
They can provide natural break points in the physical layout of the level to complement save points--which save in time, but not necessarily in space. Loading from a save point doesn't mean the player isn't still lost and might wander back to the start of the beginning of the level; a sawtooth means the designer knows for sure.
It's useful in tightly scripted "cinematic" action sequences where if the player otherwise may not know where to go or could veer off course too much and lose the immediacy of the engagement at hand.
Or, if the designer wishes to ambush or really rattle the player, certain kinds of sawtooth elements are useful to prevent the player from simply backing away from the encounter and cherry-picking the enemies from a safe distance.
The designer can also deactivate scripting or delete performance heavy entities or effects that they know for certain the player can no longer see.
This may just sound like its covering for lazy design, and while that does happen it also helps designers concentrate on crafting "the good stuff" rather than an increasing load of invisible-to-the-player housekeeping.
For the player it means a discrete point where, so long as he sees the sawtooth in advance, he knows he must be ready to progress.
For compulsive item and ammunition collecting players, approaching a clear sawtooth is a kindness; certain players hate not knowing if they'll be able to back and scrap up every last round of ammunition before moving forward.
And as previously mentioned, it ratchets physical progression through the level itself, effectively gating the play space into manageable chunks. This is helpful for designers, but aids navigation as well. In traditional "funhouse" like linear layouts, nobody wants to spend time wandering around the dead, empty portions of what they've passed through.
They're not just for single player layouts, either. For multiplayer levels whose flow tends to be circular and concentric, like a heart pumping its warring players into collision, sawtooth elements can still be useful in order to restrict two-way flow into more interesting one-way channels, say around a power-up.
To find examples of a sawtooth element, look no further than the best known FPS franchises with a linear single player or multiplayer component. A short list of recent titles would include Crysis, Call of Duty 4, Bioshock, Killzone 2, Left 4 Dead... you can find examples everywhere, once you look.
The critical view to sawteeth elements and their universal employment would be that they're a crutch that continues to prop up sloppy design and overly linear world design. So long as the kinds of things that make sawteeth such an obvious choice to use are present in level design, we'll continue to get fairly rote, linear "funhouse" type experiences.
But something as monumental as challenging concepts of linearity is outside the purview of this update--more on this sort of thing later.