What is the difference between viral antigenic drift and antigenic shift?

Both antigenic shift and drift are used by viruses to adapt to selection pressures and avoid host immune systems. 

Antigenic shift is a slow change in the viral genes over time due to replication errors and random mutations. Few antigenic shift events may allow the antibodies of the immune response to still be active. Eventually the antigenic variation will become such that the hosts immune system no longer has effective antibodies against the antigen.

Antigenic drift is an abrupt change in the genome of viruses and is a more rare occurence. It occurs due to the combination of 2 or more different virus strains. This creates a new subtype which has a mixture of antigens and so cannot be recognised by the immune system of the host. These events often lead to epidemics of flu such as the H1N1 strain in 2009.