What does LL(k) means?

The first letter, L for left to right or R for right to left, denotes the order in which to scan the source text.

The second letter denotes the derivation of the constructed parse tree. At each step in a left (L) derivation of a parse tree, the leftmost non-terminal in the tree is replaced by a terminal. In a right (R) derivation, the rightmost non-terminal is replaced. Top-down parses that scan input from left to right producing a left derivation. Bottom up parses that scan the symbols left to right produces a right derivation.

The k denotes the number of lookahead symbols needed by the parser. With k = 1, only the next symbol is needed.

Terence adds: those are the correct technical definitions. In practice LL(k) means you are building a recursive-descent parser. Recursive-descent parsers have a method for each rule in the grammar and proceed are predictive in that each rule has to predict which alternative will match. The parse proceeds from a start symbol and routes down into the various other rules depending on the lookahead. LL(k) implies up to k symbols of lookahead are visible to the parser for some fixed integer k. [Note that syntactic predicates allow you to effectively modulate k from one symbol to the entire rest of the input.]

Check out a simple LL(1) rule:

a : A
  | B
  ;

a() {
  if ( lookahead==A ) { match(A); }
  else { match(B); }
}

a -> A B C
a -> A D E