Slow, also called snare, is a Status Effect. Technically, there are two different status effects that the game calls "slow": reduced movement speed and reduced recharge rate. Many powers do both effects, but some do only one or the other.
Magnitude, Resistance, Protection
Except for Slows, all status effects work the same way. The target has both Resistance and Protection. In order for the attack to take effect, it must have a big enough Magnitude to overcome the Protection. Once the Protection is overcome, the duration of the effect depends on the target's Resistance. Attacks can stack in order to overcome a target's Protection. No Slow Protection exists, only Resistance.
PVE: Minions have a Protection of 1. Lts are 2. Bosses are 3. Elite Bosses are 6. The Purple Triangles of Doom on an Archvillain or Hero add 50 to all but Sleep while they are up. Some specific enemies are resistant to fear.
PVP: As of Issue 13, Protection does not exist in PVP, only Resistance.
How to tell if a power uses slow
Slow power icons include rings around a character, seen above.
|Tar Patch Patch Foe -Movement Speed|
Tar Patch, from Dark Miasma for Defenders, Corruptors, and Masterminds, slows a foe's movement speed, but not their recharge speed.
|Mental Blast Ranged Foe -Recharge Speed|
Mental Blast, from Psychic Blast for Defenders and Blasters and Psionic Assault for Dominators, slows a foe's recharge speed, but not their movement speed.
|Siphon Speed Ranged Foe -Recharge Speed, -Movement Speed|
Siphon Speed, from Kinetics for Defenders, Controllers and Corruptors, slows both the recharge and movement speeds of its target.