The antinode is the place of maximum displacement from the normal (on a standing wave picture that would be the x-axis), whereas the node is static - it has zero displacement from the x-axis.
In a standing wave, the antinode is experiencing the greatest net movement, or displacement, from +y to -y while the node is remaining on the x-axis.
In a picture of a standing wave the antinode at some +y can also move to -y as the wave moves, however at that particular instance in the picture the antinode is maximally displaced in "one direction" (+y). If you were shown a progression of pictures of this wave as it moved, the antinode would move from +y to -y.