Batalin-Vilkovisky (BV) quantization is way of quantizing a theory, which is apparently more powerful than BRST quantization. It has been used, for example, for string field theory, in the closed string approach.
Weinberg's book (Vol 2, chapter 15.9) is quite hard to understand for me, as I don't get the physical motivation of such approach and most of the calculations. Wikipedia is even worse for me, as it just focuses on defining operators and their properties, without giving a hint on the physical meaning of these requirements.
Why is it different from BRST quantization?