AVX are vector instructions. They work on wide register (256bit) where you can stuff 8 32bit floats (or in later versions ints) or 4 (double, or longs not sure if AVX2 or later has support for that), or 16 chars (AVX2 iirc).

APL, as an array language, should, in theory at least, especially profit from automatic vectorization by the compiler. If the auto-vectorization works well, you get get a 4-16x speed-up for free (if you don't have data dependencies).