The arm movements in the butterfly technique are similar to the ones in the freestyle stroke, except that both arms move
synchronously
rather than in an alternative fashion.
From an initial extended position, the arms first do an
insweep, then an outsweep followed by a forceful exit out of the water.
Finally they recover above the water back to their initial
position.
Swimming Video
Here's a video that demonstrates the arm movements while swimming butterfly:
Detailed arm movement
At the beginning, the arms are extended in front of the
swimmer and shoulder width apart.
They separate a little bit more so that the whole body
forms an Y-like shape.
The wrists and elbows flex, the palms face the end of the
pool, the hands start to stoke back and to converge.
When the hands arrive at the chest's level, they are nearly
together. They then start to separate again as they move
further backwards.
The shoulders clear the water, the arms extend and are
thrown forcefully out
of the water. At this time the palms are turned upwards.
The arms start to recover to the front and kind of hover
above the water. Simultaneously the
shoulders
rotate so that at the end of the recovery the palms are turned
downwards. During the
recovery the elbows are a little bit flexed.
When the arms are extended to the front and shoulder width
apart
again, they enter the water and move back to their initial position.
Some Swimming Tips
The shape drawn by the arms under water resembles a keyhole: first the arms diverge when they start to stroke back, then they converge towards the belly, then they diverge again and exit the water at the hips.
During the whole underwater phase, the arms build
up speed. This momentum helps to throw them out of the water
for the recovery.
The arms should not move all way back to the hips because
it then is harder to lift them out of the water. They should rather
finish the underwater phase by being about one foot from each side of
the body. They then exit the water and start the recovery to the
front.