This strange and redundant verb phrase occasionally pops out of the mouth of older folks from the Southern United States; it has been known to stun English teachers at fifty paces.

The phrase is basically a corruption of "Maybe (subject) could..." and is used to indicate a similar level of uncertainty and doubt. For example, let's say your cousin Jim Bob was supposed to be at your house at 5:00 to drive your Grandma Riddle home. 5:00 passes, as does 5:30; there's no sign of Jim and nobody answers the phone at his house. You need to get Grandma home, but Jim's the only one whose truck isn't up on blocks in the yard. You're stuck. "Well," says your cousin Maybell, "you might could call Aunt Gertie...maybe she seen him today bein' that she lives not ten minutes away."

In this case, the use of "might could" indicates that Maybell is grasping at straws here--she doesn't particularly think that Gertie will have seen Jim, but doesn't really know what else to propose. In other regions of the country, she might have said "Maybe you could call Aunt Gertie" (which would still involve a few extra words) or perhaps "You could check with Aunt Gertie."

As you might expect, younger Southerners tend to have this term drummed out of them at an early age so that they don't sound like unbelievable hicks (and so that the South isn't littered with catatonic English teachers).