Elixir makes a lot of the syntax of Erlang (derived from Prolog) simpler and more familiar to people working from, say, a Ruby background.
It adds better support for UTF8, better metaprogramming tools for declaring custom constructs, a standard library for things like collections and streams, proper default setup for some use of OTP patterns, and various other things. It adds a few sane default conventions for things like documentation, testing, and private/public visibility in modules.
It in turn transpiles to Erlang, so has all the same performance characteristics.