Why does the carbocation intermediate in the hydrolysis of 2-bromo-3-methylbutane rearrange by way of hydride?

A hydride shift gives a tertiary carbocation.

This reaction will proceed via an SN1 mechanism. 

Here's what happens;

1. Leaving group (Br) leaves forming a secondary carbocation and Br-

2. A methyl shift would not occur in this case since it would also result in a secondary carbocation.  However, a hydride shift would result in a tertiary carbocation, which is more stable than a secondary carbocation.  A hydrogen atom would be taken from the carbon with the methyl group, NOT the carbon with the 3 hydrogen atoms because that would result in a primary carbocation.  Primary carbocations are the least stable of the three. 

3. The tertiary carbocation undergoes nucleophilic attack by H2O.  The Br- steals one of the protons from H2O that is attached to the carbon with the methyl group.

Hope this helps!