It means you must roll 6-8 above your base base skill to get a mixed success, 9-14 a success, etc. So if your base skill is 6 for brawn and you roll two D6 resulting in a 3 and a 3 for 6, you get a mixed success.
are skills used for anything else besides this calculation?
Unless I'm misunderstanding something, if my brawn was 6 then rolling two 3s would be a mixed success, but if my brawn was 1 then two 3s would still be a mixed success? So what's the purpose of the stat being involved here?
The stat comes into play in haymakers. Often totals and base skills are calculated for whether a player can use a certain skill or the effectiveness of it.