Gazumping is when a seller, having accepted one offer, then accepts a higher offer from someone else.
A buyer who is gazumped either has to offer more money or pull out, perhaps losing money on solicitor's or surveyor's fees.
This is why you should always ask your seller to take the property off the market once they have accepted an offer (though they don't have to). Having a mortgage in principle will also help as the faster you can move to exchange contracts the less chance you have of getting gazumped.
Gazundering
Gazundering is when a buyer decides to lower their offer at the last minute — usually just prior to contracts being exchanged. This tends to only happen in a falling or stagnant market.
It may happen because the buyer calculates that the seller will have little choice but to agree.
Alternatively, the buyer may no longer believe that the property is worth what was offered — particularly when prices have been falling and a long time has passed between offer and proposed exchange.
Offer, exchange and completion
Making and accepting an offer, as well as the process from exchange to completion, are covered in our "Guide to Selling".
Something that you should do once you've had an offer accepted is ask the seller if they will take the property off the market.
While it's not in the seller's interest to do this (and they have no obligation to do so) you never know — they may say yes! If they do this greatly reduces your chances of getting gazumped.
And finally, once you get to completion — congratulations on buying your new house!