Ai is a diphthong, always long, and the second of the two grades by which the grammarians describe the strengthening of i. Where e is the first step, ai is the second, so the three sounds i, e and ai stand as one series produced by a single operation applied once and then again, rather than as three unrelated vowels that happen to sit near each other in the table.
That gives the letter a job in the vocabulary out of proportion to how ordinary it looks. The second grade is what Sanskrit uses to make a word mean something belonging to, descended from, or derived from its base, so a large family of adjectives and abstract nouns is formed by raising the first vowel of a word to this grade. The names of doctrines, schools and lineages are full of them, which is why a letter that looks peripheral in the table is not peripheral on a page of Buddhist philosophy.
Like the three other long vowels that close the vowel series it has no short partner, and none is expected. In metre it is always heavy. Its independent form appears only at the start of a word, and after a consonant it is written as a mark, which is the same arrangement every vowel in the script follows.
The independent form is uncommon, since relatively few words open on the diphthong, and a reader is more likely to meet the letter as a mark attached to a consonant than as a character standing on its own. That is true of most of the vowels after the first two, and it is why the independent series is easier to learn from a chart than from a text.