This post describes the synclient tool, part of the xf86-input-synaptics package. It does not describe the various options, that's what the synclient(1) and synaptics(4) man pages are for. This post describes what synclient is, where it came from and how it works on a high level. Think of it as a anti-bus-factor post.
The most important thing first: synclient is part of the synaptics X.Org driver which is in maintenance mode, and superseded by libinput and the xf86-input-libinput driver. In general, you should not be using synaptics anymore anyway, switch to libinput instead (and report bugs where the behaviour is not correct). It is unlikely that significant additional features will be added to synclient or synaptics and bugfixes are rare too.
synclient's interface is extremely simple: it's a list of key/value pairs that would all be set at the same time. For example, the following command sets two options, TapButton1 and TapButton2:
synclient TapButton1=1 TapButton2=2
The -l switch lists the current values in one big list:
$ synclient -l
LeftEdge = 1310
RightEdge = 4826
TopEdge = 2220
BottomEdge = 4636
FingerLow = 25
FingerHigh = 30
MaxTapTime = 180
The commandline interface is effectively a mapping of the various xorg.conf options. As said above, look at the synaptics(4) man page for details to each option.
A decade ago, the X server had no capabilities to change driver settings at runtime. Changing a device's configuration required rewriting an xorg.conf file and restarting the server. To avoid this, the synaptics X.Org touchpad driver exposed a shared memory (SHM) segment. Anyone with knowledge of the memory layout (an internal struct) and permission to write to that segment could change driver options at runtime. This is how synclient came to be, it was the tool that knew that memory layout. A synclient command would thus set the correct bits in the SHM segment and the driver would use the newly updated options. For obvious reasons, synclient and synaptics had to be the same version to work.
Atoms are 32-bit unsigned integers and created for each property name at runtime. They represent a unique string (the property name) and can be created by applications too. Property name to Atom mappings are global. Once any driver initialises a property by its name (e.g. "Synaptics Tap Actions"), that property and the corresponding Atom will exist globally until the server resets. Atoms unknown to a driver are simply ignored.
8 or so years ago, the X server got support for input device properties, a generic key/value store attached to each input device. The keys are the properties, identified by an "Atom" (see box on the side). The values are driver-specific. All drivers make use of this now, being able to change a property at runtime is the result of changing a property that the driver knows of.
synclient was converted to use properties instead of the SHM segment and eventually the SHM support was removed from both synclient and the driver itself. The backend to synclient is thus identical to the one used by the xinput tool or tools used by other drivers (e.g. the xsetwacom tool). synclient's killer feature was that it was the only tool that knew how to configure the driver, these days it's merely a commandline argument to property mapping tool. xinput, GNOME, KDE, they all do the same thing in the backend.
How synclient works
The driver has properties of a specific name, format and value range. For example, the "Synaptics Tap Action" property contains 7 8-bit values, each representing a button mapping for a specific tap action. If you change the fifth value of that property, you change the button mapping for a single-finger tap. Another property "Synaptics Off" is a single 8-bit value with an allowed range of 0, 1 or 2. The properties are described in the synaptics(4) man page. There is no functional difference between this synclient command:
and this xinput command
xinput set-prop "SynPS/2 Synaptics TouchPad" "Synaptics Off" 1
Both set the same property with the same calls. synclient uses XI 1.x's XChangeDeviceProperty() and xinput uses XI 2.x's XIChangeProperty() if available but that doesn't really matter. They both fetch the property, overwrite the respective value and send it back to the server.
Pitfalls and quirks
synclient is a simple tool. If multiple touchpads are present it will simply pick the first one. This is a common issue for users with a i2c touchpad and will be even more common once the RMI4/SMBus support is in a released kernel. In both cases, the kernel creates the i2c/SMBus device and an additional PS/2 touchpad device that never sends events. So if synclient picks that device, all the settings are changed on a device that doesn't actually send events. This depends on the order the devices were added to the X server and can vary between reboots. You can work around that by disabling or ignoring the PS/2 device.
synclient is a one-shot tool, it does not monitor devices. If a device is added at runtime, the user must run the command to change settings. If a device is disabled and re-enabled (VT-switch, suspend/resume, ...), the user must run synclient to change settings. This is a major reason we recommend against using synclient, the desktop environment should take care of this. synclient will also conflict with the desktop environment in that it isn't aware when something else changes things. If synclient runs before the DE's init scripts (e.g. through xinitrc), its settings may be overwritten by the DE. If it runs later, it overwrites the DE's settings.
synclient exclusively supports synaptics driver properties. It cannot change any other driver's properties and it cannot change the properties created by the X server on each device. That's another reason we recommend against it, because you have to mix multiple tools to configure all devices instead of using e.g. the xinput tool for all property changes. Or, as above, letting the desktop environment take care of it.
The interface of synclient is IMO not significantly more obvious than setting the input properties directly. One has to look up what TapButton1 does anyway, so looking up how to set the property with the more generic xinput is the same amount of effort. A wrong value won't give the user anything more useful than the equivalent of a "this didn't work".
If you're TL;DR'ing an article labelled "the definitive guide to" you're kinda missing the point...