The archive button does exactly that. it will take all security log items in the log and move them to an archived data file. There are a couple reasons for wanting to do this.
1) it will reset the main security log and make it faster to filter through. So it could be worth doing a periodic archive (it will amend to the current previous archives).
2) sometimes the data file, AL.dat, get's corrupted and causes issues and doing an archive can sometimes correct it because it basically recreates the file after it has finished moving it's contents to the archive file.
you can still access the archive logs through File > security > View Archived Security log.