/^[a]*$/ reads as
1) Match the start of the string,
2) immediately followed by 0 or more 'a',
3) immediately followed by "\n" (optional) and the end of the string.

When matching against "1", step (3) fails.
1) Match the start of the string -> ok, pos = 0
2) immediately followed by 0 or more 'a' -> ok (matched 0 'a's), pos = 0
3) immediately followed by "\n" (optional) and the end of the string -> fail (no "\n" or eos at pos 0)

/^[a]*/ reads as:
1) Match the start of the string,
2) immediately followed by 0 or more 'a'.

When matching against "1", it matches.
1) Match the start of the string -> ok, pos = 0
2) immediately followed by 0 or more 'a' -> ok (matched 0 'a's), pos = 0

U: Changed "followed" to "immediately followed" for extra clarity.
U: Added '"\n" (optional) and'.