Every episode in the show My Little Pony: Friendship is Magic stablishes new events, characters, and places. The MLP continuity graph is a visualization of which episodes contain references to other episodes. Earlier episodes appear on the left, while episodes which reference them appear on their right and are connected to them by lines. Keep in mind the graph only has lines which are necessary. Every episode obviously references the first one, but adding a graph from every episode to the first would add a lot of unnecessary clutter (also, keeping track of that many references is very difficult).
When you click on an episode, some of the nodes will turn green, some will turn blue, and others will be a light gray
One important thing to note is that this graph is not a chronological ordering. An episode happening before another episode does not mean there's a line from one episode to the other; there's only a line if the later episode explicitly references the earlier one.
The graph is generated from a text file which contains a list of all episodes, which episodes they reference, and a note explaining the reference (the note is particularly important, as some references are fairly obscure and need explanation). This file was created by hand by looking through screen shots of each episode as well as consulting the episode's transcript. Trying to keep track of all references is quite difficult; as such there are bound to be a few errors. If you find one, feel free to tell me, and I'll fix it when I can.
You can also copy the source code and modify the text file yourself if I forget to update this, or you want to redefine what it means for an episode to reference another episode.
All the data in the graph is calculated from this source file of references.