Sanskrit does not treat length as a shade of a vowel but as the thing that distinguishes one vowel from another, and Aa is the first of the pairs that make that principle visible. Aa is the same articulation as A, the tongue at rest and the lips unrounded, held for roughly twice as long, and swapping one for the other changes the word rather than the accent. The varnamala is built out of such pairs: short and long a, short and long i, short and long u, and then the two vocalic liquids in their short and long forms, before the compound vowels close the series. Because the pairing is systematic, the writing is systematic too.
Where a consonant sign already carries the short a without any mark, the long aa is written as a separate stroke attached to the sign, and that stroke is the first vowel mark a learner meets. The independent letter shown here is the form used only when nothing precedes the vowel, at the head of a word or after another vowel where no consonant intervenes. The distinction between the independent letter and the attached mark holds for every vowel in the script, but it is easiest to see with aa, because the difference between the presence and the absence of a mark is here the difference between a short vowel and a long one, and nothing else about the syllable changes at all.