When we look at “a” we pronounce it /ā/, or “ayy.” This is the first letter of the alphabet, and when looking at the isolated letter, we’ll refer to it by its name: the way we say it when we begin to recite the alphabet. This is known as a long vowel sound, because it says the “name” of the letter. The same goes for the other vowels.
A short vowel sound is a vowel sound that does not follow this rule. When reading a word that uses a short vowel sound, will say the sound that the letter can make that is not its actual name. So in the case of “A,” the word “main” might have a long “A” sound because we pronounce the “A” as /ā/, whereas the word “man” has a short vowel sound.