+1 is the enhancement bonus of the weapon: it means that, while wielding said weapon, the character will add 1 to both his attack bonus and damage.
+11/+6 are the number of attacks the character can do while using a full-round action.
The first attack will strike at +11 bonus, the second at +6.
Hope it helps. (also, forgive my bad English)
Yeah. The +1 is the enhancement bonus from it being a magic weapon. Enhancement bonuses range from +1 to +5 normally, since +5 is the cap for enhancements on a weapon. In addition, a weapon can have up to a +5 equivalent in special abilities (like a Flaming weapon). This add +1 to both attack AND damage, but the attack roll bonus does not stack with the +1 bonus from a Masterwork weapon (all magic weapons are masterwork).
As you gain BaB you gain Iterative attacks. At 6 BaB, you gain a 2nd attack at -5 (+6/+1). At 11 BaB, you gain a third, at a further -5 (+11/+6/+1).
The character in your scenario has at least a +6 BaB (to gain an iterative), a +1 enhancement from the weapon (for +7) and then likely has 18 Dex (+4) for a total of +11, which on an iterative gains a -5, for +6. +11/+6.
Here's hoping I didn't make it more confusing in the process there.