Here is a list of typical LoL terminology. You'll be seeing these words come up in just about every single LoL game you play, so knowing them leads to better teamwork, which is what the game is really about.
MIA: An enemy champion is missing from the lane. Be aware of your surroundings and keep an eye on the mini-map. You'll find that situational awareness is key in this game.
Gank: What an enemy champion usually does once he's MIA. He'll try to sneak into a lane and get a 2 vs. 1 kill on an enemy champion. The lanes that get "ganked" the most are the top lane and the middle lane (generally referred to as "top" and "mid")
Pings: Signals on the mini-map. Signalling could mean many things, and there are two types of them. There's the general "ping", which shows up as a blue alert signal on the mini-map, and a "careful" ping, which shows up yellow. The general ping could mean many things, i.e. attack, obtain a "buff" (get into that in a sec), attack the Dragon, take down a tower, etc. If someone pings, they're usually implying that they need assistance or are trying to get your attention. If a yellow ping goes off near you, you should retreat asap. This means that enemy champions are converging for a gank on you in most cases, or that a fight is about to go sour.
Buff: There are 3 "buffs" in Summoners Rift. There's the Red Buff, Blue Buff, and Baron buff. The red is obtained by killing the Elder Lizard, and grants the user increased damage (applies a damage over time affect on the enemy) and slows enemies hit by a flat %. The Blue Buff, obtained by killing the Elder Golem, increases your mana regeneration significantly and reduces the cool downs on your spells, generally allowing you to cast your spells more freely. The Baron Buff increases your health regeneration, mana regeneration, attack damage and ability power. This is obtained by killing the Baron neutral creep, an extremely important team objective. The Baron Buff goes out to the entire team, which is why it's so important. These buffs will usually give you the edge you need to better yourself in the "lane" or against an enemy champion.
Bot: Referring to bottom lane.
B (or Back): An easy way of letting your team know you're going back to the fountain to shop or regen your health/mana when you're running alarmingly low. I recommend that you "back" regularly if running low on health. Handing kills to the enemy is no bueno. That means he has more time to gather minion kills and gain experience on you, not to mention the gold and experience you give him upon death.
Farm: What a player should be doing in the "lane phase" (early game). By farming, you're getting the last hit on minions, earning you gold and bonus experience. The general goal of farming is to have more gold and experience than the enemy champions in your lane. The easier it is to farm, the easier it is to gain gold/experience, the easier it is to defeat your enemy.
CS: Creep Score. This is earned by getting the last hit on creeps. The higher the creep score, the more gold and experience you generate. This comes with good "farm". Beating your enemy in CS gives you a solid advantage over them in most cases, unless they're "feeding" off you or your allies. (CS can be seen on the scoreboard next to your kill/death/assist).
Feeding: What a player does when they die repetitively to an enemy champion. By "feeding" and enemy champion, that enemy becomes much much stronger, and tends to "snowball" into the middle and late portions of the game.
Snowball: This is a bit tougher to explain. A champion that snowballs means that, through getting "fed" and having good "farm", said champion can get their middle and late game items sooner, allowing a very strong advantage over their enemies. Snowball champions are extremely dangerous, but if shut down early game, tend to plateau at the end of the game.
Drag: Referring to the Dragon neutral creep found in the river near bottom lane. Killing the dragon earns your entire team +190 gold and a small amount of experience. Keeping track of the Dragon creep and obtaining it regularly earns your team an advantage over your enemy.
Creep: Minions, whether they be neutral, ally, or enemy. The Neutral creeps can be found in the "jungle", including the Dragon and Baron. Creeps will attack you (aggro) if you attack an enemy champion with an auto attack whilst near said creeps. Nailing an enemy champion with a spell does NOT cause these creeps to aggro onto you, so choose your timing wisely. Sometimes the extra damage caused by a few creeps will be the difference between life and death when in a fight with an enemy champion. The Jungle creeps (including Baron and Dragon) won't aggro onto you unless you attack them.
Jungle: The forested areas of the map, where all the neutral creeps and Buff creeps can be found and killed for bonus gold/experience. Some champions don't need to be in a lane at all, but can sustain themselves perfectly off of the jungle, as well as ganking lanes often. Once you become higher level you'll find that a jungle champion is a crucial dynamic in, quite literally, every single game you'll play. Learning that role is a whole other area of expertise, but is incredibly fun nonetheless.
There's just a basic list of you'll run into in the LoL lingo (both in game and out). Hopefully you find this helpful when reading guides and playing them games