carbocation rearrangement
Carbocations are so eager to be more stable that they will sometimes rebuild their own skeleton to get there. A carbocation rearrangement is when a positive charge that lands on a less stable carbon hops to a more stable position by having a neighboring atom or group slide over. It is as if a person standing in an uncomfortable spot lets the person next door swap places so they end up somewhere comfier.
There are two common moves. In a hydride shift, a hydrogen atom on the carbon next door migrates over to the positive carbon, taking its bonding pair of electrons with it; the positive charge is left behind on that neighbor. In a methyl or alkyl shift, a whole carbon group does the same. The key is that the migrating group brings its electrons, so the cation moves from, say, a secondary carbon to a more stable tertiary one. The shift happens only when it leads to a more stable (or comparably stable) carbocation; the molecule will not rearrange into something worse.
Rearrangements are a famous trap and a famous clue. They explain why a reaction can give a product whose carbon skeleton is rearranged compared to the starting material, a result that baffles students who forget cations can shift. Their appearance is strong evidence that a carbocation intermediate formed (so the mechanism is SN1 or E1, not SN2 or E2, which do not allow rearrangement). Reactions that avoid carbocations, or use alternatives like hydroboration, are chosen partly to sidestep this scrambling.
When 3-methyl-2-butanol is dehydrated, the initial secondary carbocation undergoes a hydride shift to become a more stable tertiary cation, so the final alkene's double bond ends up in an unexpected place.
A single hydrogen slides over, the charge moves to a more stable carbon, and the product skeleton changes.
Only the electrons and the migrating atom move, and only toward greater stability; a carbocation will not rearrange to form a less stable cation, and reactions without a carbocation intermediate (SN2, E2) never rearrange.