BC - ballistic coefficient. How your bullet reacts to the air. It's a combination of weight and shape of the bullet. Higher is better for long-range shooting.

gr - grains. The weight of a bullet. 5.56x45mm (standard AR-15) uses bullet weights as low as 55gr, and as high as mid-70s. Lighter bullets are easier to push faster (which is why AR-15 rifles tend to be pushing bullets to 3200fps with pretty minimal recoil).

fps - feet per second, usually measured at the muzzle. Bullets slow down as they head down range, due to air resistance.

Bullets don't travel in a straight line; the second they leave the barrel, gravity is acting on them, and they're getting pulled down. So you're always shooting in an arc. For short ranges, that arc is pretty negligible. For a long range shot, you may need to be pointing significantly higher than your target. In the case of the rifle pictured, you should need to aim about 13' above a target that's 1000 yards away in order to have your bullet hit (that's your "hold over"). If there's wind--and there almost always is--you're going to need to compensate for that by aiming to the right or left ("windage"). A spotter makes this much easier; your spotter should be trainer to read winds. They should also be trained to see where the bullet hits, so you can make an adjustment, e.g., one target to the left, one half target low.

(I've only gotten to shoot longer range a handful of times, the last time with a spotter, and the spotter made it so easy to get on target. Check out 9HoleReviews on YouTube for examples of how that works with a really excellent marksman and spotter.)