Why do SN1 reactions prefer tertiary carbons?
The intermediate in an SN1 reaction is a carbocation. The stability of that intermediate determines how favorable that particular reaction is, so a more stable intermediate means a more favorable reaction. 

Carbocations are quite unstable on their own, but the inductive effect of nearby C-C bonds provide some electron density to balance out the positive charge, making the carbocation intermediate more stable. Tertiary carbons have the largest number of adjacent C-C bonds, the largest inductive effect, the most stable carbocation intermediate, and are thus favored in SN1.