XLA: Accelerated Linear Algebra, I guess it's kind of a backend/compiler that optimizes Linear Algebra/Deep Learning calculations with some very interesting techniques, among them fusing kernels
JAX: In some sense syntax sugar over XLA, but a better way of describing it is Composable transformations + Numpy + some Scipy. The composable transformations allow you to take derivatives (be them single, multi or vector valued functions and also higher order derivatives), JIT a function (which is them compiled to XLA), 2 forms of parallelism (vmap and pmap) and others, while being compatible with one another and with both TPUs, GPUs and CPUs