MK is a very solid character. He has very few unfavourable match ups, but they are all doable.
As for the why, I can give a little bit of insight into that.
MK is one of the fastest characters in the game. He has immaculate grounded mobility, and while his air speed isn't as impressive, he can still zone well through the use of his multiple jumps and disjointed aerials (that, unlike Ike's and Zard's, are quick to come out, so they are very good for reacting to opponents' movements and are harder to bait and punish).
MK is adept at killing both horizontally and vertically, and has many reliable set-ups into doing so. For example, his throws can set-up for DC, bair, or dair off of uthrow, or edgeguards or tech chases dsmash/DC. Speaking of his throws, MK's throws are also very good at low percents, for tech chasing and gaining stage advantage. He also has very little trouble securing a grab, thanks to his movement speed as well as his JC or boost grab (similar to Sheik's).
His nair is good at intercepting aerial approaches and edge guarding, as well as escaping comboes. People like to say MK's green button is really good. They're not wrong. Nair -> dtilt -> nair is hella tight.
Speaking of dtilt, it's similar to Marth's in that it's good against grounded opponents and, depending on the hitbox, pokes away (tip), or pops up (hilt) for an aerial follow-up (making it harder to DI).
MK's recovery is long. It's not the best recovery in PM, but he has neat tricks with the shuttle loop and drill rush is good for catching opponents off guard (also good for extending comboes on stage and for catching people on edge of dash dance/landing). He has multiple jumps so intercepting him from below is trickier. Recovering from below the stage is normally a bad position to be in but not for him because shuttle loop is so hard to challenge.
His dash attack is a good move. He leaps forward so it can catch people at the end of their dash dance or as they are landing. It also crosses up shields, which really helps his shield pressure game since many of his moves are shield grabbable. Out of run he also has dtilts, dsmash and usmash, which are really good for tech chasing/killing and intercepting aerial opponents respectively (skipped talking about dtilt since I already covered that). Usmash leads to nice follow-ups without good DI/SDI, but even so, he gets a lot of advantage anyways.
His shield pressure isn't the best, but crossing up opponents isn't that hard (through dtilt, dash attack, being generally fast, nair, and DC) and helps as I've already said.
Another thing that really helps him out in my opinion is his ability to trap you in at the sides of the stage. All factors considered, MK has many ways to push you to the edge, through tech chases, nairs, dtilts, dash attacks and others. Once you're at the ledge, it's hard to get back in a lot of cases. His dtilt is good at controlling the ground, as are his dash dance, dsmash, and grab, and his fair/nair/bair are good for catching opponents escaping in the air.
*** One of MK's biggest assets is the large bubble he controls in the center of the stage. He threatens a lot of space and it's hard to escape once he's cornered you.***
DC is really
really really good. I'll leave it at that and let
_Chrome
explain it since it's kind of his personal stamp on the character (afaik).