In this episode, we find out how our little 5 man band gets formed for real! It starts with both the badminton club and the Choir club getting their death warrants handed to them by the acting principal, the witch from vice! It seems that the principal is one huge softy and was allowing the badminton club to continue on its merry way with only one member against the school's rules, and the choir club has a rash of defections now that the concert is over and Konatsu's brother doesn't feel beholden to continue on and takes his friends with him. Leaving the club "officially" at three members (though we see Sakai's club resignation form repeatedly in the episode...) Both club presidents vow to keep their dreams alive. Taichi recruits Wien to join him in badminton, but still needs three more people. Konatsu has an idea: They will play a game of badminton, and if Taichi wins, the choir club members will join his badminton club and if he looses he will join the choir club. At first, it look like it is just Sawa and Konatsu playing against Taichi, then Sakai surprises the girls and shows up to play too, seeming to cement her as a member of the club, or maybe just as a friend... Then Wein shows up to help Taichi. Now the stakes are enough for the winner to officially form a club, conveniently filled with the five main characters...
How does it end up? If you haven't watched, I won't spoil it... Unless you read the quote below (in white-text), which is from a guy over at CR explaining what he thinks the title means. So, if you don't want to know about the rest of the episode, don't highlight the white text.
Basically, it's a pun based on the new club's title. You'll find Japanese people rather enjoy puns and wordplay, so stuff like this isn't uncommon.
There are a lot of ways to conjugate Japanese verbs, one of which is a "list form" using -tari. You can think of it a bit like the gerund in English. If you forgotten what that means, it's just adding "ing" to a verb. For instance, "I'm reading, writing, and chewing gum." Tari is slightly different, but this should give you the general idea.
The new club's name is "Singing, Dancing, and sometimes Badminton Club". On the application form, it wasn't written using the -tari construction, but it could easily have been.
So, I *think* the title "Tari Tari" is a little joke that the club will be doing a little bit of everything.
This makes a lot of sense and explains why the episode titles are always "X-ing and Y-ing":
Ep 1: Running and Inviting
Ep. 2: Gathering and Struggling
Ep. 3: Swinging and Meeting
Ep. 4: Getting angry and Dancing