Everyone in an Alliance, including Provisionals, can enter the Alliance Quarters, use the Alliance Chat, and use the buffs from the Photon Tree.
Members can do everything a Provisional can do, and use the Storage (assuming they have Premium).
Officers can do everything a Member can do, and can add new Players to the Alliance, upgrade and water the Tree, access all Team Expansion settings, kick non-Officer Players from the Alliance, and promote and demote Players between Provisional and Member.
The Leader can do everything, including promoting Members to Officers, demoting Officers to Members, changing the Team Settings (ie. Flag, log-in message, etc.), and initiating Unions.
Also, just as an additional note, if the Leader has not logged in for 30 days, then an Officer can take over the role of Leader.