I have a vague notion that a tank is a character which can take a lot of damage, an assassin is one that's good at killing other champions, a DPS does a lot of damage over time, a Mage works from a distance, a Carry is weak at the beginning and stronger later on, and so on.

What I'm looking for is something that explains these roles in a little more detail.

Is there something like that around here?

Try this: http://www.leagueoflegends.com/board...d.php?t=110065

If that isn't enough explanation, I'm sure we can provide more

Not sure, but I will expand on them a bit.

Tank: Generally needs to be able to initiate a team battle OR have some form of strong crowd control (CC). High health is just necessary as they will be in the thick of things for the longest and potentially be focused, but high health alone won't make a tank (as they will just be ignored otherwise). Good tanks can both, off tanks often only have a single one of the above attributes.

Examples: Alistar, Shen, Rammus

Assassins: Generally strong 1v1 champions that rely on stealth. Work primarily as ambushers. Often weaker in team fights due to being generally "bursty" in damage and lower in health. Good assassins will spend mid game popping out during ganks to help get kills and late game jumping into team fights after the other team has committed (bad ones tend to get kills by playing mop up when your team has been killed but left the enemy weakened). As their stealth abilities can be shut down by a couple of items 9wards/oracles), these see less play in higher level games.

Examples: Evelyn, Twitch

DPS: Damage per second. They do the most damage over the course of a team fight generally. They tend to either have readily spammable abilities or abilities that compliment thier auto-attacks. this allows them to consistently do a sustained high amount of damage.

Examples: Tristana, Master Yi

Mage (Nuker): Generally built to do massive damage quickly, these are almost always centered around AP builds. They tend to have a set combination of abilities that will destroy most champions in a single blast, but are then ineffective while they wait for their stuff to come off cooldown.

Examples: Ryze, Annie

Carry: General terms for your most effective late game player. They "carry" your team. While in the strictest sense, this generally refers to someone who is weak in the beginning and very powerful at the end (Tryndamere), that may not always be the case. Many champions can "carry" if they are fed, so I often see it used for the most effective/dangerous player on the opposing team.

Support; Any character who's primary focus is to buff your team or debuff the other team. They tend to do little in the way of damage, but increase your teams survivability and disrupt the other team.

Examples: Janna, Soraka, Morgana

Most champions can be built for several of these roles and many can be built as hybrids, falling somewhere in between roles. Your best bet is to read some of the guides in the guides and strategy section for champions you are curious about to get a feel for what roles most champions are being used in.

Kat, Shaco, and Akali are also assassins, and seem to be the more popular ones these days. Kat is probably not so much of an assassin, but she still counts in my book.

Can someone give me an illustration as to how a tank can force a battle to happen in a particular place?

(And what exactly is crowd control? As in, what kinds of abilities or item powers are CC abilities and powers?)

Only certain tanks can FORCE a battle to take place. Ones like Malphite and Amumu basically attack the other team and CC them, allowing your teammates to get the advantage in the fight. Specifically Malphite's ult allows him to charge towards a certain location (hopefully a group of enemies) and knock them all into the air, stunning and damaging them. Amumu has it a little tougher since he has to use a combination of skills but basically to the same effect.

Mostly tanks try to initiate a fight by pretty much running in head first and drawing as much focus as they can. As the other team unloads on the tank his teammates use the opportunity to come in and attack while the opponent's attention (and damage) is elsewhere.

CC= Crowd Control. CC is basically any spell that will stun, slow or snare an enemy. Just about every character has one or more. These have tons of applications and go a long way towards deciding who wins the fight.

Hope this helps

Assassins don't need to be able to stealth, it just makes it easier to pick up on more quickly. Champions that have blink type abilities (whether they let you jump to a target location or enemy) can also help build an assassin, as well as some other abilities. Assassins need to be able to get in, kill someone, and get out.

Akali is a prime example of an assassin, even ignoring her stealth (though it's great for allowing her to survive after jumping in).

Tank, in turn I could ask you if your parents dropped you when you were a baby because you are wrong.