Huh... I don't play adventurer's league but going with my gut, I would assume anything that you could hire someone for, say for example the Rogue generally provides the services of scouting, disarming traps, opening locks and things of the sort, the Fighter generally provides the service of guard, muscle, marksman or the sort, the ranger does mostly the same as the fighter but he's also generally a guide and a hunter not to mention they are known for crafting tools and even weapons, I'd also assume all crafting is a service and the bard's music counts as a service of entertainment and so on.
The list of things that could be considered a service are infinite but if I were to guess that's there to force players to RP why they are giving something away rather than it just being like "You're the one that would make the most optimal use of this item, so have it.", this is good, Paladins & Rogues normally don't get along but the Rogue is the most likely to find whatever the Paladin needs so this could force them to interact and come up with a reason to get along besides we're just in the same party, it's also great for Rogues since they are the most likely to find epic loot they can just sell it to their companions if they do not meet the requirement of providing a service and that makes them rich.