Why do people say Mitt Romney has swiss bank accounts?

Because it is in his actual financial disclosures. He actually tried to hide them when he initially disclosed the financials then had to go back and amend them. Quote from the article I am linking:

The discovery that the Romneys had $3 million in an account with the Swiss bank UBS came only after the Republican presidential candidate released his tax returns for 2010 on Tuesday. The campaign had maintained that it was not necessary to disclose the Swiss account because Romney's money manager, Brad Malt, had shuttered it in early 2010.

EDIT: BTW, Midwestern below is full of sh*t. Yeah Obama didn't publicly release his grades but NO PRESIDENTIAL CANDIDATE EVER HAS. George W. Bush's only became public because someone leaked them to the NYTimes. Bush initially refused to release them himself in 1999. Nor has Romney released his college grades. So at least Obama has given more disclosure than Romney has. See for yourself: http://factcheck.org/2012/07/obamas-sealed-records/

EDIT #2: First of all, you asked for proof of the accounts, not reasons for why it was relevant. Second of all, are you really comfortable electing a guy to be President if he doesn't even know where his own money is? I honestly don't know if it would be better for him to be lying about not knowing or actually not knowing. If he is not lying about it, then he literally couldn't keep track of his own fortune of $250 mm, how do you trust him to take on the job of keeping track of our national budget? "Oh, wait, I didn't know my financial advisor did that!" sounds awfully close to "Oh wait, I didn't know my economic advisors did that!" Not comforting.
Third of all, the main problem here is just Romney being completely secretive, which if he had nothing to hide, should not be the case. We don't know when the Swiss account was opened or who opened it (the "blind trust" that opened it this account also JUST HAPPENED to invest in Trigg Romney's hedge fund too). Only two reasons to open a Swiss account as an American: 1)hide assets 2)hedge US dollars against depreciation with Swiss Francs. Assuming no mischief, it still makes no sense for Romney to open an account all the way in Switzerland just to get Francs. With the level of wealth he has, he could easily have bought government bonds and FX contracts in the open market. Warren Buffet has NEVER had a Swiss Franc account, so why did Romney need it?

This is off topic, but something else we actually never hear about is the fact that Romney has over $100 million in his IRA account. How does an account that has a max of $30,000 allowable contributions annually grow that much? One very likely reason is that his Bain fund would buy a company, issue shares to partners that could be put in the IRA account, then undervalue those shares by many times the realistic value to get under the max threshold. These are the typical kinds of games financial guys like Romney play constantly to skirt the letter of the law while absolutely spitting on the spirit of it. To me, it speaks of moral flexibility which I don't want in my President.

A $3 million Swiss bank account appeared in his 2010 returns, then winked out of existence in 2011 after the trustee closed it. Ed Kleinbard, a professor of tax law at the University of Southern California, says the Swiss account “has political but not tax-policy resonance,” since it—like many other Romney investments—constituted a bet against the U.S. dollar, an odd thing for a presidential candidate to do. The Obama campaign provided a helpful world map pointing to the tax havens Bermuda, Luxembourg, and the Cayman Islands, where Romney and his family have assets, each with the tagline “Value: not disclosed in tax returns.”

http://politifact.com/truth-o-meter/...

fully cited report

EDIT: "the trustee for the Romney family’s financial investments -- Brad Malt of the law firm Ropes & Gray -- acknowledged it in an on-the-record call with journalists on Jan. 24, 2012.

Malt said on the call, "Yeah, it occurs to me that one other question that came up. … Why is there a Swiss bank account listed on the Romney's tax return? It is listed because I set that account up for diversification in 2003, when I became trustee of the blind trusts. It is a bank account. Nothing more, nothing less. An ordinary bank account. It earns some income, which is fully reported on the Form 1040 in the (2010) tax return. You'll see approximately $1,700 of interest earned by this account, which is reported. The tax is fully paid just as if this were a U.S. bank account, nothing more complicated than that."

from above link

"Tell a lie enough times and it becomes the truth." -- Joseph Stalin

Romney told the press to cram it when they demanded more of his returns. The press responded that this refusal was proof that Romney was doing something illegal or unethical with his taxes.
The logic of the press, No records: something illegal.

Obama refuses to release any scholastic records from Occidental College, Columbia University, or Harvard. The press says that these records are not necessary because Obama must have been an outstanding student.
The logic of the press, No records: outstanding student.

The democrats say that like the democrats say a lot of things. It's just a lie. They say it do people think that Romney is not close to home but he is very close to home, in fact if anyone is not close to home it's Obama he may not even have been born in America. Romney 2012!

Troll.

because it's something that appeals to "envy voters" instead of "issue voters"...

Why do they say anything they say? Their nuts. That's why.