The Lytic Cycle is the viral replication process that rapidly kills a host cell. During the lytic cycle, the nucleic acid of a virus takes control of the activity of the host cell. The nucleic acid directs the host cell to make more copies of the virus. When the virus is finished making new virus particles, it kills the host cell, by bursting the cell walls in order to release the new particles to infect other cells.
The Lysogenic Cycle is the viral replication process in which a virus does not immediately kill its host cell. During the lysogenic cycle, the nucleic acid of a virus attaches to the host cell's chromosomes. A host cell may reproduce itself many times, by cell division, with the prophage still attached to its chromosomes. Eventually a stimulus, such as radiation or a specific chemical, jolts the prophage off the host chromosome.