Can someone help me understand a few concepts please?
AD and AP carries, etc - what do those mean?
How do I know who is what in game and how much attention should I be paying to things like this?
I know these are very broad questions... thx.
"Carry" as its used nowadays, is basically synonymous with "damage dealer". It used to mean something a bit different, but thats how the term is used in LoL now. So a carry is a very different role than a tank (whose job is to start and control teamfights) or a support (whose job is to buff and heal their own team).
You can either be an ability power (AP) carry or an attack damage (AD) carry. Hybrid carries generally do not exist.
AP Carries become stronger by stacking ability power. Common items here are Rabadon's Deathcap (pure damage), Rod of Ages (mix of damage and health), Void Staff (damage and magic penetration), and Zhonya's hourglass (damage and defense). AP carries are generally strong early game and fade late game unless heavily fed. They generally, but not always, do their damage in large bursts. The damage from AP carries is mitigated by magic resist, but NOT armor.
The most common AP carries are: Annie, Brand, Orianna, Fiddlesticks, and Malzahar. Morde is usually built as an AP Carry/tank combo and Akali is usually built as an AP carry/assassin combo.
AD Carries become stronger by stacking attack damage. They usually rely heavily on autoattacks, so getting attack speed and crit chance increases is also a good idea. Common items are Infinity Edge, Last Whisper, Brutalizer, and Phantom Dancer. Madred's Bloodrazor also works and allows the AD carry to hybridize a bit by doing some magic damage. AD carries are generally weak early game and get stronger late game. They generally do sustained damage over time instead of in bursts. The damage from AD carries is mitigated by armor, but NOT magic resist.
The most common AD carries are: Ashe, Corki, Vayne, Tristana, and Caitlyn.
Teams generally should have at least 1 AD carry and 1 AP carry. That way the other team can't mitigate your damage by only stacking armor or MR, but must stack both to really reduce your team's damage.
Ranged AD carries are usually preferred to melee AD carries since they are more difficult to kill. You should be identifying and trying to kill the other team's carries first. They do the damage, but typically dont have many defenses, so kill them fast. At low levels of play you can play melee AD carries and get away with it (the classic example being Master Yi) since teams dont target carries as well, but at high levels of play somebody like Yi will get targeted and focuses too quickly to be real useful to the team in most cases.