In ARAM all players are randomly given a champion from their available pool (including free rotation). Playing ARAM matches earns you points so that you can occasionally reroll what you have, and you can also trade your champion with an ally as usual.
The map is Howling Abyss, which is a single lane that has a few bushes on the sides. Once you leave the spawn area you can't shop, so you must buy items when you die (not dying is not always a good thing, dying at the right time is strategic) and it doesn't heal you either, nor can you recall (though the animation will now play).
The mode focuses on team fighting since there's only one lane, and there is no jungle. In Legend of the Poro King you get to choose your champion instead of randomly I think, and your Summoner Spells are only Poro Toss and To the King. They are easy and fun modes.
I recommend trying out some ARAM; you may love it! (Disclaimer: It may sometimes be frustrating due to the random nature, as sometimes you lose very badly in champ select)