The other guy covered what it is. As for how to get it now...

If you find someone selling a carry and you can pay their price, that's the easiest way. Be sure to do all the negotiating with the in-game chat tools; if any part of it takes place through other channels, Blizzard definitely won't protect you if you get scammed. If you can join a guild that has already cleared ToS on heroic, and if they'll take you, that's also easy, but it's relatively unlikely at this point and they'd probably expect you to at least pull your weight.

If you can't do either of those, you'll have to do it in pickup groups. A lot of good groups will ask for AOTC and good gear before accepting you because they want to make it easy on themselves. Some groups might accept people without that stuff, but they're more likely to fail. Heroic KJ is no joke for a disorganized group. It is theoretically possible to do it in a PUG, I did it three weeks ago and one or two people in the group got the achievement in addition to me, but it's not easy.

If you want to get AOTC:ToS, then gear up fast, get your tier set bonuses from Normal ToS and Heroic NH if they're good for your class, join any group that'll take you, and start your own if you have to. Theoretically possible but not likely or easy. Antorus comes out on November 28 so you have less than two weeks. On the other hand if you just want AOTC: Antorus, you'll have several months to get that.