Slow, snare or root are words in Diablo games describing a debuff effect that decreases the target's movement speed, and/or attack speed. Often used in boss fights, to kite monsters around, or in PvP, for the same reason.
A slow debuff can be applied through a direct skill or environmental effect, or through one or several AoE effects.
A root effect is different only in that the movement impairment is 100%. The target is stuck to the ground. A root status effect rarely means the attack speed is decreased.