Lol is a 5 vs 5 multiplayer game.
The match takes place in a map called "Summoner's Rift". At 2 angles of the map there are the 2 teams' bases, with a "nexus" (a circular structure) at their center, protected by 2 towers*. The goal of the game is to destroy the enemy nexus before your opponents can destroy yours to win. A little ahead of the nexus there are 3 inhibitors (circular structures, they look like a mini nexus), one right in front of the nexus and the other 2 at the sides. These inhibitors mark the beginning of the 3 lanes: Open "routes" that connect the 2 bases designing a sort of diagonal reticle on the map. In between these 3 lanes there's a jungle with walls that force a certain pathing inside it and some spaces occupied by monsters (they don't attack unless disturbed) and a river perpendicular to the lanes crosses the map in the middle (it contains the 2 biggest monsters that give a meaningful advantage to the team that kills them).
From behind every inhibitor periodically mini monsters are spawned: They are called minions and they walk down their respective lane until they find something that belongs to the enemy team, which they start attacking (usually this something is enemy minions, so around the middle of the lanes there's a mini battle between the 2 teams' minions).
In front of every inhibitor, at the start of each lane there's a tower, 2 more towers for each team are at 1/4 and at 1/2 of each lane. Towers attack the first enemy thing that goes under them.
So for now each team has: A nexus, 3 inhibitors, 9 towers, infinite minions. *= 11 towers. I forgot about nexus towers, mb! :p
Every player will choose a character to play, called champion. The foundament of the game is that you need to help your minions advance, so both you and them can hit enemy towers (the tower is attacking the first enemy that goes under it so if you make your minions advance first it will hit them and leave you alone), and preventing your opponent to do the same to you. Of course the most effective way to prevent opponent from doing something is killing them: When someone gets killed he has to spend several seconds in base, unable to do anything on the map, and then he has to walk all the way back to his tower to return defending it.
Every champion has a particular set of characteristics and 4 abilities. If you right click on something your character will fire a "basic attack", which usually reflects the weapon they are holding (a champion with a bow will fire an arrow, a champion with a sword will swing his sword, a champion holding a wand will fire a magical projectile from his wand and so on). Pressing q,w,e,r will make the champion use the respective ability tied on that key.
Pressing P when you are in base will open the shop: There are many items that will improve different characteristics of your champion: Attack damage will make his basic attacks hurt more (no matter if the champion fires arrows or balls of fire with his basic attacks, they all get increased by attack damage or AD), armor and magic resistance will make it so the champion gets damaged less by physical or magic damage respectively. To know if an ability does physical or magic damage you need to read the description of the ability, which will say something like "does x magic damage / does y physical damage". Ability power increases the damage of some abilities (others are increased by attack damage): To know how an ability gets more damage read its description, there will be something like "does x (+y) magical /physical damage" if that y is green you want ability power (or AP) if it's orange you want attack damage (or AD).
Based on these characteristics and on what his abilities do every character has a different role: A champion with ranged attacks (bows, guns..), orange abilities and /or abilities that increases his attack speed (how many basic attacks he can fire in one second) will want to increase his attack damage and attack speed as much as possible and do damage continuously (ADC), a champion with green abilities at range will want to increase his ability power and cool down reduction (how often he can use abilities) (mage), a champion with low damage but high defensive characteristics will want to increase his defenses and bring chaos in enemy team /protect his allies (tank), a champion with abilities that heal and shield will want to focus on helping allies (support ).
Periodically the game gives a little amount of gold to every player, but to be able to buy items from the shop comfortably you have to gain gold in an active way. Gold can be gained by killing your enemy champions (controlled by your opponents), killing enemy minions, destroying enemy towers and inhibitors and killing the monsters present in the jungle.
Since there are 3 lanes with minions and a jungle with the monsters there are 4 sources of gold.. For 5 players. So, lol players came up with a strategy to avoid sharing the same source of gold between 2 players: We send a person in a lane with another, and that person is supposed to don't kill minions and try to leave kills on champions too, effectively putting his share of gold in the pockets of one of his allies. That person takes the role of the "support" and often plays champion that depend on allies (healers, shielders, some tanks). With time a special line of items got created to give a little more periodic gold so the support can have a little more gold too. Often he stays with the ADC, cause ADC champions tend to be very weak at the start and the support protects them. The person that takes his gold killing the monsters in the jungle is called jungler, and in addition to killing monsters he can now and then show up in one of the lanes and be like "surprise! I came to help my ally!" (this is called "gank") . The other roles take the name of the lanes they are defending (upper lane =top. middle lane =mid, Lower lane =bot. Usually occupied by ADC + support)
Pressing b will teleport you to base after a channel. Staying in the base heals you and gives you back mana (mana is needed to use abilities, at least for most champions, and it's a blue bar under the health bar).
I think my wall of text is done, I tried to enter into details as much as I could while keeping it "simple" (as simple as lol can be). You should really try it out for yourself though. I started playing with my boyfriend and my brother (after months of them trying to convince me) and now I play more than them and even surpassed them on the competitive ladder ;) if you want some practical introduction (play together)feel free to ask :) it would be a nice surprise for your bf I'm sure
Edit: I missed aspects part. Aspects, or skins, are a cosmetic element. They are totally useless to gameplay but they are really cute (for example my favorite champion is Lux, a girl dressed in some kind of armor-dress with light abilities. With skins I can get her to run around in a pink custom sailor moon -like and shoot pink stars xD totally useless, the abilities are the same.. But cuute _ )