In the lytic cycle, a virus that has invaded and entered a cell takes over the cell's replication mechanism. The virus makes viral DNA and viral proteins.
The virus then lyses (breaks open) the cell membrane, allowing the newly produced viruses to leave the now disintergrated host cell to infect other new cells.
The lytic cycle is considered the main method of viral replication. It is even more common than the lysogenic cycle. It has helped scientists understand better how the immune system responds to pathogens.