What is suspend?
Suspend mode is a special low-power mode, often used on laptops, that preserves the contents of RAM while conserving power.
There are two main forms of suspend - suspend-to-RAM and suspend-to-disk (also known as "software suspend" or "hibernation"). Suspend-to-RAM uses more power, but is almost instant. Suspend-to-disk, on the other hand, uses no power (the system actually powers off), but takes longer to suspend/resume.
You can find more info in this wiki page.
When you click on suspend, everything on your system goes into a low-power mode, except for memory which is placed in such a state that it will retain its contents. The peripheral bus lose power and devices attached to your client are also suspended. Typically, it should take around 1-3 seconds to enter suspend (or suspend-to-RAM) state.
On mobile clients, like laptops, you can enter a suspend state (or sleep) by simply closing the lid, or choosing suspend from the power menu options. To wake up the system from suspend, you simply have to open the lid.
On some models of laptops the lid switch does not enable a wake. In that case, you could hit any key or the power button to wake the system from suspend. On desktops you could hit the dedicated sleep key (if there is one) on the keyboard, or simply push the power button to wake up the system from the suspend state.