To the cross-platform part OpenGL you need to use the correct platform-specific library to setup an "OpenGL context". This is a painful process, which is why libraries such as GLUT, SDL, GLFW exist.
So where does EGL enter? It was initially conceived as the equivalent of WGL/GLX/etc for embedded systems (OpenGL ES). However, OpenGL ES is slowly gaining momentum on desktop systems: Android/iPhone/etc development environments and WebGL is built on OpenGL ES and EGL. Recent Ati drivers ship EGL and so will Mesa in the future.
Wayland is using EGL instead of GLX simply because GLX is tied to the X11 API (and Wayland is not running on top of an X server).