A blend space is a concept used in animation scripting where several animations are asssigned a position on a graph, and one or more input parameters calculate what mix of which animations should be playing at the current moment.
Here we see an example of a One Dimensional blend space. Speed is controlling where the blend is calculated to be on the graph. The bottom node represents the idle animation, where speed is equal to zero. Above that are the Run, Walk and current blend position (in orange).
A 2D blend space is exactly what it sounds like - many animations can be mapped onto a graph with two dimenstions rather than just one. A common example of this would be a characters base movement. Below we can see many different animations have been plotted on a graph representing direction along one axis, and speed along another. Using this the scripter is able to create a state for an animation state machine that takes into account these two inputs to play a blend that will see the character turning and running in the correct way.