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.