The Disney movie suggested the reason for the many cups was that every day was an "Unbirthday", when in fact in the books, it was because the Mad Hatter had argued with his friend Time, and it was now always six o'clock, time for tea.
Later on, the Hatter, March Hare, and Dormouse are brought the Queen of Heart's courtroom when Alice is put on trial for supposedly humiliating Her Majesty purposely.
Together, the two commonly engage in tea parties; most of which are to celebrate their "unbirthdays".
While the Hatter is loud, eccentric, and insane like the rest of Wonderland's residents, he is also rather charming and can be mild-mannered from time to time, particularly when dealing with visitors such as Alice.
Though a recurring character, in a sense, most of the Hatter's roles in the show were brief and minor.
However, he played his largest role as a major supporting character in the episode "In the Bag".
As a result, he takes out many wheels and springs with a fork in his attempt to fix it.
He adds ingredients to the mixture: the very best butter, tea, two spoons of sugar, jam, mustard (which is rejected, since it's too silly, even for him), and lemon.
When Mad Hatter bows down the Queen of Hearts one of her Cardguards pokes him in the rear causing him to scream and lands near her who then tells him to take off his hat making him jump out of his shoes.
When asked where he was during the incident, the Hatter explains he was home drinking tea to celebrate his unbirthday, which reminds the King of Hearts that it was the Queen's unbirthday as well, thus causing the Mad Hatter and March Hare to bring the trial to a halt to celebrate.
According to Hatter, he and the March Hare never get compliments on their singing, and they're usually the only attendants at the frequent unbirthday parties, apparently making the duo outcasts in the realm of Wonderland.
This is most likely due to their overbearing antics and personas, as well as the fact that they're both, especially the Mad Hatter, troublemakers, albeit innocently so.
Soon the party is once again interrupted by the White Rabbit.