He has something sorely lacking in modern politics: authenticity. It doesn't matter if he's an authentic lunatic, he's still more appealing to voters than the coached robots the parties usually produce.
I think this is exactly it... Everyone else is kissing babies, he's leaning in for a kiss and saying "yikes, that's an ugly baby, I'll pass". Now, everyone might agree that it's an awful thing to say, you may even think "what's he talking about? that baby is adorable!" but the thing is... no one else is being honest. Watching everyone else is a little like watching one of those TV singing competitions, you know someone is going to overact during the performance, they're going to throw in an out-of-place, unnecessary falsetto, and the judges are going to pretend that they just witnessed the birth of a once in a lifetime talent. Watching Trump is like going to a bar and watching a band that, objectively, blows... A band that makes music you would never actually buy... BUT a band that gets everyone in the room singing along when they cover a classic. Yeah, they suck... yeah, they shouldn't be making music... but you know what, for tonight they're entertaining enough and they're fulfilling a need. Trump would probably make a pretty awful president, but at least he's shining a light on how much of a PR puppet everyone else is, and he's saying things that no one else can really say. For example, "I can buy and sell each and every one of you, not just because I have the money, but because you'd LET ME buy you and sell you to the highest bidder" is something that none of the other candidates can say because it's probably true of just about all of them, Trump can say it because, as well as he may be doing, he's basically a kamikaze approaching the target... The worst thing that can happen to him is that his campaign crashes and burns sooner than expected, in which case, who cares? To him, this campaign is (probably, I'm only guessing here) the equivalent of painting TRUMP on the side of his 757... it's just branding. If it all comes crashing down he can go back to being a successful billionaire, and he can go back to making quiet contributions to anyone he needs to buy so that whatever tract of land he needs to turn into a golf course, or a hotel, or anything else becomes just that. Trump is doing well because, he may be saying beautiful things or he may be saying awful things, but he's saying them with no filter... everyone else is a PR puppet kissing babies and standing on bales of hay to give empty speeches.