Similar to blocking in fighting games, the block mechanic is Champions Online is a single key press (shift by default) that puts you in block mode when held. While in block mode, you absorb significant amounts of damage, can avoid status effects, and (depending on your stance) regenerate additional energy when attacked.
Every character can use standard block by default. It is shown in the first button in the first hotkey bar. There are a number of shield type powers you can learn that replace your standard block, and enhance your blocking ability both in defensiveness and by adding some nifty special effects.
To put it in terms of hard numbers, here is some basic analysis. These numbers come from using the high damage blue laser in the PowerHouse. A "Slotted" block refers to one of the block enhancing shields.
BASE DAMAGE: 714
Regular Block: 238 (66.67% dmg resistance)
Slotted Rank 1: 204 (71.43% dmg resistance) +4.76%
Slotted Rank 2: 178 (75.07% dmg resistance) +3.64%
Slotted Rank 3: 155 (78.29% dmg resistance) +3.22%
In addition to the damage resistance, if you have block mode up while hit with a big knockback, hold, root, or other status effect power, the block will completely diffuse it most of the time.
The most important time to block is when you see a villain charging up a major attack. This is signified by a large shaped icon appearing over the mob's head. When you see that icon, you may want to get block mode going as soon as possible. Once the attack lands, you can go back to attacking. You will learn that some villain types have worse special attacks than others, and some you might not be too worried about.
Another good time to block is while you are landing right in the middle of a pack of bad guys. This is especially true if you are low on energy or have a lingering shield. The first few hits will charge your energy bar while leaving you mostly unscathed. Then you can unleash your own pain back at them.