The way I understand it is as follows (corrections welcomed!):
Alitalia has always been a state-owned carrier, and that for most of its post-1970 history, its has been losing money year after year. (1950's and 60's were an economic boom time in Italy). It is not competitive with other European airlines because of very socialist-style burdensome work rules whereby a person once hired can never be fired, cannot have their pay cut, cannot work more than "X" hours per week..etc..etc.
To try to get back in the black, Alitalia initiated the "TEAM" concept in 1996. Alitalia TEAM is basically an airline within an airline. Alitalia refer to TEAM as
"the company for operation of low-cost medium and long-range routes"; in reality it was basically a sneaky way around the work rules that allowed Alitalia to hire new university graduates that are paid less and work harder. You'll notice now that all aircraft have the red "TEAM" square and somehow the TEAM concept (supposedly an airline within the airline) has become standard practice on all Alitalia routes. In theory its the first step towards a privitization of the airline, but no significant steps have been taken in this direction as of yet.
So "TEAM" is really nothing more than a cost-cutting measure. BUT, a highly effective one. In 1996-1998 Alitalia did make money for the first time in decades. They would have made money in 1999 if it werent for the Malpensa airport debacle. Now that they have to pay back KLM a cool $98 Million, don't look for a profit in 2000 either.