A lytic cycle is when a virus infects a cell, immediately makes more copies of its genome, expresses the proteins needed to make new viral structures and then causes lysis of the cell (break open), thereby spewing out new viruses to infect more cells.
In contrast, in a lysogenic cycle, a virus enters the host cell but doesn't replicate its genome. It normally integrates its genome into the chromosome of the host and lays dormant...its genome is copied along with the rest of the host's genome (that way it propagates).
At some point the virus can exit dormancy and go lytic.
