First of all - the name "synaptics" is historical and now woefully inadequate. On Linux, we now rely on the kernel to address device-specifics and simply use the event API. In fact, synaptics is just like evdev with different features. (Note to non-Linux users: we still have the backends for hardware communication in the driver as well)
So whenever we talk about "synaptics devices", the "synaptics driver", or "synaptics features" in X, we mean "touchpad". All of the features are described in the man page and can be set either as an xorg.conf option or at runtime by tweaking the properties (with xinput or synclient). I'll brush on the capabilities exposed by the GNOME tool, for the KDE tool check the comments, I'm sure Kevin Kofler will point to them as usual.
Furthermore, I won't list the various options required to configure all this - simply look it up in the man page and you may find some other gems in there too.
The most commonly used touchpad feature is likely edge scrolling. Four edges are defined on the touchpad and movement outside of these edges is interpreted as scrolling. By convention, scrolling in X is buttons 4,5 and 6,7 for vertical and horizontal scrolling, respectively. If movement in the scrolling areas is detected, the driver converts the motion into a number of button presses for these scroll buttons.
Vertical and horizontal edge scrolling is hardcoded to only work on the right and the bottom part of the touchpad. They can be enabled separately and independently, though the GNOME GUI we have for it ties the horizontal scroll method to the vertical scroll method.
Edge scrolling is quite configurable, allowing for minimum and maximum speed settings and even pressure-dependent scrolling. Of course, the distance required to emit one scrolling event is configurable as well. None of these tweaks are exposed in the GNOME GUI.
Two-finger scrolling is the basic multi-touch feature that the driver provides. If two fingers are detected on the touchpad (you will need the hardware capabilities to do so), vertical and horizontal two-finger movements are converted into scrolling events. Provided the scroll methods are activated of course. The GNOME GUI allows for either edge or two-finger scrolling, the driver could provide both simultaneously.
Now, the interesting thing about two-finger scrolling is that it is usable on touchpads that only support single-fingers as well - through the two-finger emulation. If enabled, the driver tries to guess based on the width of the finger whether it is a single or dual-finger input and then trigger the required bits.
Other than that, two-finger scrolling is rather unexciting, it just does what it says on the box. As with edge scrolling, the minimum distances for a scroll event to be generated is configurable (but not in the GUI).
Tapping is the action of quickly putting a finger down on the touchpad and lifting it again. Multi-finger tapping is the same action with more than one finger. Synaptics currently supports up to three-finger tapping plus corner tapping. Each multi-finger tap can be assigned a different button, the default the GNOME tool assigns if tapping is enabled is 1/2/3 finger tapping to left/right/middle. Again, multi-finger support relies on your hardware.
Tap-and-drag is automatically enabled, whereby tapping an object, then dragging it with one finger "locks" the mouse button on the object.
Corner tapping works similar, but instead activates hot-zones in the corners of the touchpad (defined by the edge settings). Each corner can also be assigned a different button action. Corner tapping is not exposed in the GUI at this point.
Click fingers are similar to tapping in configuration and effect, but the trigger is different. The ClickFinger actions are executed when the left button is pressed while fingers are down on the touchpad. So if you leave two fingers resting on the touchpad and press the physical button, the configured action is executed. This can be quite useful for those that cannot or do not want to use tapping but still require left/right mouse button presses from their touchpad.
Similar to the edge and two-finger scrolling but detects circular motions instead of up/down and left/right motions. This works quite similar to the iPod interface. Depending on the trigger, a circular motion started in that trigger area (e.g. top right corner) will initialize the scrolling behaviour. Note that the circular scrolling events are generated per angle motion, i.e. by changing the radius of the circle you can change the speed of the scrolling.
For scrolling, synaptics has coasting available as well. If enabled, scrolling continues even if the finger has lifted off the pad - provided enough force was to begin with. So if you quickly swipe two fingers up/down, scrolling will only stop once you tap the touchpad again. Coasting is disabled by default and judging by my computer, Firefox seems to be slow enough to give it a coasting feel anyway ;)
Also note that this isn't a physics model, it's a simple start/stop mechanism which arguably isn't quite as useful as a physics model may be.
We don't have any of the well-known pinch, rotate, swipe, etc. gestures yet. The main issue here is not the driver itself, it would be reasonably easy to add the bits to the driver but we can't do much with it. We have no meaningful way to transmit the gesture data to the client. So it's down to hacks like in the infamous elantech driver that shipped with the Dell Minis. Unfortunately, having the driver generate keystrokes like Ctrl+ to zoom in is hacky at best and nightmarish at worst.
We really need to update the middle-man here (the X server) to provide this information to the client so they can do the appropriate stuff with it. Alas, this work is taking a while.
I just wanted to add this to have one more place to say it: SHM config doesn't exist anymore. You will need X server 1.6 or later to run the current versions of synaptics and if you see a message asking you to enable SHM configuration, your distribution may need updating or the program that pops up this message may need to be fixed.