Spiral beings are viruses, destroying whatever might be a threat to them, and Lagann is a rootkit, hijacking other files. Lordgenome and the Gunmen are freeware antiviruses, which are constantly running and able to quarantine the spirals/viruses, but not get rid of them completely. Beastmen are the core files that allow the Gunman programs to run. Grappals are programs created by the spirals/viruses to resemble the Gunmen/antiviruses. The anti-spirals are all files for a single commercial antivirus, which is inactive until it detects a certain number of spirals/viruses. However, the user set this number too high, and so the program doesn't act until it's too late and the spirals/viruses are capable of completely overwhelming it. Eventually, when the spiral beings/viruses run free for long enough, the computer's user will have no choice but to reformat, bringing an end to the universe within the computer and creating it anew.
