From Halopedia, the Halo wiki
No-scoping is the act of shooting an enemy with a scoped weapon, but without using your scope. The term typically applies to scope-less shots pulled off with a Sniper Rifle, Type-50 particle beam rifle or Binary Rifle; less often, it may refer to scope-less headshots performed with a Magnum, Spartan Laser, Carbine, Needle Rifle, Battle Rifle, or Designated Marksman Rifle .
Learning to no-scope is a definite must for advanced players. In situations where a charging enemy must be quickly neutralized, switching weapons or zooming in would waste valuable seconds and likely result in the sniper's death. No-scoping is a valuable skill to possess in a repertoire, especially when armed primarily with a sniper-only weapon.
As with most advanced skills, practice is essential to master this skill. So if you don't get it right away don't give up; just keep on trying.
When an enemy is approaching you with a Battle Rifle, Magnum, Needle Rifle, DMR or Carbine, don't waste time trying to scope. Just keep your cool and remember that you only need one shot, while they need a minimum of seven rounds to kill you. Line your reticule at head level, and if possible, strafe to line up the shot and fire.
That is the most common situation to use no-scoping, and since one of the best ways to counter a sniper is with the Battle Rifle, it's also a pretty common scenario.
Arguments against no-scoping
Since ammunition for sniper weapons tends to be very rare in the Halo games, each Sniper Rifle bullet is extremely valuable. Those who disapprove of no-scoping tend to argue that instead of wasting ammo on a charging enemy by using the no-scoping tactic, it would be better to switch to another weapon that can kill the threat, without wasting the "ever-so-precious" sniper ammo.