What exactly does the couple do during the cake cutting?

It really depends! If there are no special cultural traditions, then you will cut the cake, pose for some photos to remember the moment by. 
My husband is Polish and so we did a little tradition where the venue brings the married couple 2 shots - 1 a shot of vodka, and the other, a shot of water - they mix them up, so no one knows which is which and then we drank one each - whoever gets the vodka is supposedly the one who 'wears the pants' in the relationship. Things like this are fun, but of course not necessary. If you like the idea of something like this though and it's not part of your own cultural background - borrow someone elses! Google 'wedding cake cutting traditions' and see what comes up ;) Have fun with it! 
- Danielle :)

Hello, this is the time to take more amazing photos, the bride and groom stand next to each other and both take hold of the knife. You pose for more photos before you glide the knife through the cake.You take out a slice and and attempt to feed each other, some brides and grooms have fun and try to smoother it on their face. The cutting of the cake is such a locely part of the wedding. Well worth having a lovely looking and delicous cake. Thank you for your question. If we can be of service please call us on 9585 6549 . CW cakes Cheltenham.

Stand by with a spoon each and feed each other the first bite. One of many occasions to be shared over cakes together . 

Hi & Congratulations on your pending wedding,

Great question, traditionally the happy couple will have photos cutting the cake, celebratrating a toast their wedded bliss in front of the cake, you could be feeding each other a piece of cake which has become more a modern tradition. Why not start your own special tradition.

Good Luck 

Kathy Always Time For Cake - Melbourne