Teepan, the / is similar to the *nix file root only in this case it's the tmsh module root. Whilst you can get away with not using it if you don't move around the tmsh module (and command) heirarchy you can't if you do. This only applies if you are actually in the tmsh. For instance, from the HMS Bash shell;
tmsh
...(tmos)ltm
...(tmos.ltm)modify pool...
...(tmos.ltm)save /sys config << Not using /sys at this point will fail as we moved to the ltm module earlier
tmsh
...(tmos)modify ltm pool...
...(tmos)save sys config << / not required as we are at the root of the module heirarchy