Welcome back
Dungeons which you were familiar with now have 3 "levels":
normal < heroic < challenge
Normals and heroics work the same that the ones you used to know.
Challenge is completely new type which
doesn't offer ANY gear. It was introduced to allow people who like hard dungeons compete with each other by timed runs. Most people don't bother with it cause they offer no actual rewards.
Raids that you were used to now have 4 "levels":
LFR < Flexible < Normal < Heroic
LFR is not "real" raiding, it was introduced only to allow people who can't commit do scheduled raiding to see the content. Don't expect any challenge from it. It's just go-kill_boss-get_loot machine.
Normals and heroics work the same that they used to in wotlk. The only difference is that 25 man versions now drop the same ilvl as 10 man versions.
Flexible is completely new mode, on similar difficulty level as WotLK Naxxramas. (yeah, MoP normal mode is a bit harded than WotLK normal mode). It's main feature is no fixed raid size. You can bring any number of people from 10 to 25 and bosses will scale to the size of your group.
Most people focus on 2 of the raid "levels": either do flexible and aim for normals, or do normals and aim for heroic.
Scenarios on the other hand are completely new feature that is not connected in any way to raids or dungeons. They are basically 3-man dungeons with no fixed group roles (tank/healer etc.). You also complete them by following objectives rather than simply killing stuff.