Theory is that businesses hire people at wages which are equal to what the business thinks they're worth, ie how much they'll increase revenue.
If a fast-food franchisee thinks that an extra person to work the register would be worth six bucks an hour of increased business, they'll hire someone for six bucks an hour. If the government says they need to pay someone at least ten dollars, then they just won't hire that extra person, and take less business but higher profit. So by trying to increase wages, the government would wind up costing a bunch of people their jobs.
It's hard to measure empirically (like basically everything in the social sciences), but I think most studies show a small effect on employment and some studies show no effect. The minimum wage keeps coming up not so much cause it's a great tool to help poor people, but because it's politically feasible.