Markovnikov's Rule

Markovnikov Rule predicts the regiochemistry of HX addition to unsymmetrically substituted alkenes.
The halide component of HX bonds preferentially at the more highly substituted carbon, whereas the hydrogen prefers the carbon which already contains more hydrogens.
Anti-Markovnikov

Some reactions do not follow Markovnikov's Rule, and anti-Markovnikov products are isolated. This is a feature for example of radical induced additions of HX and of Hydroboration.

Mechanism

The proton adds first to the carbon-carbon double bond. The carbon bearing more substituents forms a more stable carbenium ion; attack of bromide ion follows in a second step:
Markovnikov
Radical reactions require an initiation step. In this example, a bromo radical is formed.

The reversal of the regiochemistry of addition is the result of the reversal of the order in which the two components add to the alkene. Radical addition leads to the formation of the more stable radical, which reacts with HBr to give product and a new bromo radical:
Anti-Markovnikov