A team event is one that involves teams of people playing against each other. This is more advanced than an event that involves just individuals playing each other (or pairs of individuals as in a doubles event).
Team events typically involve more than one club where each club offers one or more teams to play in, say, a county league system. But this is not necessarily the case and clubs can set up their own team event.
The process to set up a team event is the same as any other event, involving an event manager to define the event, event administrators to run the event and event organisers to prepare the draws (if any) for the event.
But it also involves the team manager to define the teams and team captains to gather and manage their squad and the club's booking manager to control and set the parameters for who can pre-book courts and when.
So a team event will involve various disciplines from start to finish and the broad schematic outline of this process is given here using a county league event as an example: