SeeD,
Balamb Garden's Special Force.
SeeDs are trained into battle and are send all over the world.
They are payed mercernaries because NORG wanted to make money out of this coorperation.
Unlike NORG, Cid's true interest wasn't about the money.
SeeD, as said above, are sent around the world to fight and become stronger for the final battle.
The Final Battle consist of Defeating an Evil Sorceress.
At the time this was established, the only sorceress in the world were Adel & Edea.
Of those two at the time, Adel was the only one evil.

This is bassicly what SeeD is.