I don't get it.
1) Palin helps McCain with the conservative base, unlike Tom Ridge or Joe Lieberman. Reviled though these voters may be in many quarters, their turnout is imperative to McCain having any shot at winning in November. If they stay home, he loses, no matter how much appeal his ticket has to independents or wavering Democrats.
2) Palin isn't, like Mitt Romney, another rich white guy with a family name in politics. She's from a middle-class background and a mother of five. While this may not really be relevant to being elected vice president, it's not necessarily bad electoral politics.
3) While Palin won't appeal to many or even most of the millions of women
and men who voted for Hillary Clinton, if she peels off even a few of them in key states, that could be significant. More importantly, there are also millions of women, such as suburban married women, who might find Palin appealing. Women voters are not confined to the urban upscale professional women and working-class women who comprised among the most ardent constituencies among Hillary's supporters.
4) In her brief political career, Palin has a record of challenging entrenched interests in her own party over corruption issues. This is significant since the GOP presently has a poor record on ethics, which is a turn off to independents and rank-and-file Republican voters who might otherwise turn out for McCain. Palin beat Murkowski for governor and has pushed Stevens to come clean. Compare this to Obama's rise in the Chicago Democratic political machine.
5) Of the four politicians on the two major tickets, Palin is the only one who is genuinely an outsider. Although this plays into her weakness of a limited resume, it may have appeal for some voters. Her resistance to the corrupt party machine in her home state adds to this. Heck, not being in the United States Senate might be a good enough credential for some people.
6) Her biggest weakness is of course her absolute dearth of national or international experience. It appears that the McCain camp has decided that conceding this issue that they could have used against Obama is worth whatever positives they think Palin brings to the campaign.
7) Ideologically, her most controversial position is likely her support for teaching creationism alongside evolution in the public schools. Out of the mainstream though this may be, I doubt that too many people who find this a basis to oppose her were likely to vote for her anyway. For everyone else, it's a minor issue or a non-issue. Your local school board member has more input on this than the vice president or president.
McCain's only chance of winning is taking a gamble, since this year sucks for Republicans thanks to the GOP's poor showing in the White House and in Congress recently. Maybe it works, maybe it doesn't, but he had to try something, and apparently Mitt Romney or Tim Pawlenty weren't it. Lieberman would've been bold, but then McCain loses the base, which, as noted above, means he loses almost automatically.
9) I think what the McCain campaign specifically hopes to achieve is to target suburban married women, which would be the key to winning the white vote and the married vote, since he's going to carry white men and married men anyway, as the GOP always does. If McCain can win the white vote and the married vote by large enough numbers, then it doesn't matter how much he appeals to anybody else, because those constituencies are large enough and tend to have high enough voter turnout to help him carry the dozen or so key states necessary to achieve a majority in the electoral college.