The altitude is a line from some vertex to the other side of the triangle (first pic). The median is a line from some vertex to the middle of the side across from it (middle pic). The bisecting angle or whatever it's called is simply a line cast in the direction of 1/2 the angle (last pic)
Actually, I found a much better image than my mspaint thing.
Consider this triangle ABC
The line from A, straight down is the altitude. The one from A to the middle of the base (close to the a), is the median, and the one that is 1/2 the angle of BAC is the bisector.