A top-down parser that uses a one-token lookahead. The first L indicates that the input is read from left to right. The second L says that it produces a left-to-right derivation. And the 1 says that it uses one lookahead token. (Some parsers look ahead at the next 2 tokens, or even more than that.)
A grammar G is ambiguous if some sentence in L( G) has more than one rightmost (or leftmost) derivation.
This is the (0), (1), (k) or (*)-syntax you see after the names of these two general algorithms, such as LR(1) or LL(k). k usually stands for 'as much as your grammar needs', while * usually stands for 'this parser performs backtracking', which is more powerful/easy to implement, but has a much higher memory and time usage than a parser that can just keep on parsing linearly.
The basic requirement for the compiler is to simply stop and issue a message, and cease compilation.
Parsers should preferably be LL(1)