Someone in a 2nd dimension world (which is impossible for us to really imagine) wouldn't have a concept as time as we know it. You're taking time for granted as always being...time! This explanation is saying that the 4th dimension is what we call time, because the 4th dimension is a "line"- a connection, between two different "points," or presents, or realities, in the 3rd dimension. So right now I'm typing while listening to Weird Al, and later on I'll be eating ice cream from the container. The 4th dimension of my reality is the "line" that can be drawn from me typing to me eating, which we call time. But in the 2nd dimension, which like the 4th is also a "line" (a connection between two 1-dimensional points,) their "time" is a "fold" in their own dimension, which causes their position in their 2nd dimension to seemingly instantly change.
Does that make sense? Of course, I don't take everything in the animation to be automatically accurate, but I like the metaphors he draws. The ant is especially good and another look at it might help you (Tarzanman) understand the supposed relationship between the first few dimensions better than my (attempt at an) explanation.
Now I'm gonna take some ibuprofen. A lot of it.