Hit refers to physical damage that occurs as a result of an attack made with melee or ranged weapons.
If the difference between the mob's level and your level is greater than 2, then the formula for calculating your base miss rate against that mob is:
with single-wielding: 2% + (Mob Level - Your Level) * 2%
with dual-wielding: 21% + (Mob Level - Your Level) * 2%
Applying these formulas gives the following base miss rate for a Level 80 character:
v. Level 80 mob: 5.0% / dual-wield: 24%
v. Level 82 mob: 6.0% / dual-wield: 25% (level of most heroic bosses)
v. Level 83 mob: 8.0% / dual-wield: 27% (level of raid bosses)
Thus, if you are a Level 80 character with no talents increasing your chance to hit, you need a Hit Rating of 247 (8.03%) to never miss a shot against a Level 83 boss (or skull mob) with a special attack or single-wield auto-attack.
Melee attacks divide into two categories: auto-attacks (white attack/damage) and special attacks (yellow attack/damage).
A "soft" cap is the point at which your yellow attacks will always hit and more hit rating has no effect on them. A "hard" cap is the point at which your autoattacks will always hit and more hit rating does absolutely nothing for you.
All level 80 physical DPS:
Single-wielding auto-attack: 263 Hit rating
Dual-wielding auto-attack: 885 Hit rating