I think that there is no better explanation than this:
The Astral Dimension is a parallel dimension where the soul exists outside of the body.
I don't think he should forget everything everything he learnt in the astral plane, I think his knowledge remains with his soul and not with his body.
This explains the hospital scene:
When Stephen Strange was injured as a result of his conflict at the New York Sanctum, he stumbled through a portal into the Metro-General Hospital. There, Strange left his physical form by simultaneously assuming the astral form and entering the Astral Dimension, rendering his body unconscious. During this time, he helped Christine Palmer perform surgery on him by re-emerging in the regular universe in his astral form. Palmer was shocked by this stunt and assumed Strange was dead at first. However he was followed by the astral form of Lucian, one of the enemies he had just overcame.
They battled it out in the Astral Dimension, and some of their actions had weak and muffled effects on the regular dimension. While they fought, Palmer continued her attempts to resuscitate Strange, using duel defibrillators. As it happened, this fact was able to energize Strange's astral form. Strange realized he could use that power against Lucian while in the Astral Dimension, so he asked Palmer to keep using the defibrillator. Strange forced the power through Lucian's astral form, completely incinerating him in the process.
And in this source, it is explained a little bit more about the astral plane in the marvel universe:
In the Marvel Universe, the Astral Plane is the realm of minds. Telepaths are able to access the Astral Plane by projecting their mind onto this realm, more commonly known as Astral Projecting, this also allowing them to enter the minds of others.
Doctor Strange has practiced astral projection since his inception in 1963
Edit: If you ask why the things in the normal dimension were affected by Strange's actions in the astral dimension I found a really good theory in an answer here:
Your physical body vibrates at a certain density, a lower density than your energetic or astral body. So your physical body is fully capable of grasping a cup, opening a door, and walking around for example, because those objects are on the same plane as your physical body. Your astral body is energy without physical form and is roaming around on a different plane. Just as in your physical body you cannot “touch” anything on the astral plane, so too on the astral plane you cannot “touch” anything on the physical plane.
In other words, you have to be in the same frequency with the plane you want to alter.
My assumption is that when astral forms of Benedict and the other villain where hitting each other hard, somehow somewhere their frequency matched to the objects in the actual plane (where their bodies lie), thus altering the objects state on impact. Remember, frequency of vibrations changed due to several reasons like stress, love and happiness too.
