log*(n) is the number of times you need to apply log to n to get a number < 1 (although since it's only ever used for complexity analysis, you can use any other constant instead of 1; 2 also seems popular).
If we take logarithms to base 2, log* is 1 in the range [1,2), 2 in the range [2,4), 3 in the range [4,16), 4 in the range [16,65536), 5 in the range [65536,265536). An n for which log*(n)=6 is unimaginable huge: considerably larger than 1018000(!)