The primary purpose is to serve as an instrument to proclaim The Gospel of Jesus Christ. All other goals of the band are considered "Proper" when their ultimate goal is observed.
The brass band may be seen as an evangelical tool to generate a spiritual response by helping to set the mood & enhancing a spiritual message.
Member retention. Many members were introduced through to the Salvation Army through the brass band, & some may have strayed if not for their attachment to the band.
Drawing attention & Publicity for fundraising
Christian fellowship for players
The brass bands also seem to be more popular in the United Kingdom than in the United States.
Here is some more information about the Salvation Army Brass Band :