People commonly interpret this as being multiple timelines, or the meta-time in which history may be changed.
But more seriously, you would have physics defined in 5 or more dimensions with 2 or more being "time like". (Oh look, It's in Wikipedia!)
Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue. This corresponds to the existence of a "time-like" direction. A metric with multiple negative eigenvalues would correspondingly imply several timelike directions, i.e. multiple time dimensions, but there is no consensus regarding the relationship of these extra "times" to time as conventionally understood.
You would have events plotted in 5 dimensions with rules explaining the allowed relationships between them. These rules may be different along the different kinds of time. But, like space dimensions are all the same, I like the symmetry of two time dimensions being the same too.
How this would seem to someone inside it, I'm not prepared to say※. The common wisdom is that it would not be "interesting" like our universe.
(I'd copy the illustration but it doesn't like SVG it seems. See the link in the paragraph above, please.)
But another idea would be, not a branching universe, but a 2D plane on which the world line of an object can choose a line. Just as forces change the direction of motion in 3 spacial dimensions to pick out one possible line, the time direction might be one chosen line out of infinite possibilities. A different kind of force would alter the trajectory. That would leave the world behind, as everything else continues on the old time direction. This describes what's normally considered parallel universe, and logically that's indeed what a parallel universe is. Perhaps you can combine separate history and branching history by having specific things cause splitting rather than everything causing splitting.
※ update: Greg Egan is writing a novel set in a universe with two space dimensions and two time dimensions. See his page for material including the mathematics of spacetime in his universe! This material was made available in December 2016. The novel will be out in mid 2017.
It might be tempting to think that with two dimensions of time, the history of any particle, or person, would cease to be linear and would take on some kind of planar aspect. But in fact, there is no reason why objects shouldn’t trace out essentially one-dimensional world lines through space-time, much as they do in our own universe. The difference that arises from having a second dimension of time is that of all the straight lines that pass through a given point, more of them would count as possible world lines.