When I read this verse, because I believe that the Holy Ghost is given by the priesthood ordinance of laying on of hands, I do not see Jesus literally breathing on His disciples. However, I think it is worth looking at these verses to see what the purpose might be for saying Jesus breathed on them.
I think there was a teaching purpose for it. When I think about why John might have wanted to use this idea of breathing, the thing that comes to my mind is a phrase “the breath of life” from Genesis 2:7:
And the Lord God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul. (Genesis 2:7)
I think breath was associated with life and John wanted to teach that when Jesus told them to receive the Holy Ghost, He gave them a portion of spiritual life in a way they hadn’t experienced before or thought possible, and the only way to express what it was life was to compare it to receiving breath.
I have to echo that. When I receive the Holy Ghost, it does fill me with life, and it seems to throw over my perception a hopeful optimism that I would hate to be without. It's like seeing the world in color when you're used to seeing in black-and-white.
What is it like for you?