Blitzball is a fictional sport played in Tidus' time and 1000 years back in Spira. It's a game like soccer, where two teams try to score goals on opposite sides of a sphere of water. It's actually pretty complicated to play, and I'm terrible at it; in all my times of playing Final Fantasy X, I have never beat the Luca Goers. Final Fantasy X has an in-depth tutorial on blitzball that covers moving, passing, shooting, breaking, and more. The player is forced to play one game of blitzball, and if you enjoy it, you can play it at save points for the remainder of the game. Tidus and the party will come across players you can recruit to your blitzball team throughout all of Spira. You can play games, practice, and level up your players. Blitzball is a game within a game, and a player can get hardcore into blitzball. Unfortunately, it just has never interested me.
Now, let's talk about what blitzball means to Tidus and Spira.
Before coming to Spira and becoming one of Yuna's guardians, blitzball was Tidus' life. Following in his father's footsteps, Tidus was a star player of the Zanarkand Abes. He was good at blitzball, and was a celebrity in his home town because of blitzball.
In flashbacks, you can see Tidus trying to play blitzball, and his father watching, judging, and then showing off. I've always wondered why Tidus wanted to play blitzball since he hated his father so much. Knowing his father was a professional player, I would think Tidus would want to have nothing to do with anything that had to do with his father. And yet, Tidus followed in his father's footsteps. I think Tidus played blitzball to rebel against Jecht. Growing up, Jecht kept telling Tidus he couldn't do things in blitzball, and that Tidus would never be as good as he was. All of his cut-downs had to do with Tidus crying, or not being good at blitzball.
You with a woman? You can't even catch a ball!
By playing blitzball, and being good at it, Tidus proved his father wrong.
On the boat to Luca, when thoughts of his father are angering Tidus, he starts kicking a Blitzball around. Tidus attempts the Jecht Shot, the Sublimely Magnificent Jecht Shot Mark III, a shot Jecht told him he could never do. By beating down verbal attacks from Jecht, Tidus can master the Jecht Shot. What's interesting is memories of his father were sparked by just coming upon a blitzball. Blitzball makes Tidus think of Jecht.
I think doing something his father told him he could never do makes Tidus happy. I think he also just found joy in playing.
When people were scared for their lives, and Sin was a constant threat, the people of Spira turned to blitzball for happiness as a distraction. It gave them something to do and be excited about. In a way, blitzball becomes like that for Tidus, too.
When Tidus floated to the shore of Besaid, he was thrilled to find a blitzball floating in the water. It was something that connected his world to the one he found himself in, and for a brief moment, it allowed Tidus to forget his troubles. Tidus played with the ball he found, quickly impressing Wakka and the Aurochs with his obvious skills. Tidus landed himself a position on the Aurochs' team, earning the respect, admiration, and friendship of Wakka, and allowing him to travel with Wakka, Yuna, and the others to Luca. This of course leads to Tidus becoming one of Yuna's guardians, meeting his father again, and playing out his destiny. It's funny to think that blitzball connected him to all of that.