First of all, male doges are neutred by removing their testicles, and females are neutered (also called spayed) by removing their ovaries and uterus. This puts an end to their ability to reproduce and have babies.
These gonads (the testicles and ovaries) normally produce a lot of hormones that perform a lot of roles in the body, and without them there are some consequences. Firstly, the risk of certain types of cancer can be higher, but at the same time, the risk of other cancers is less. Secondly, there can be some behavioural changes as the hormones testosterone, oestrogen and progesterone can affect aggression, energy levels and general “mood”.
Mostly though, there is very little effect and you wouldnt notice a difference in your dog, especially if the procedure (which is entirely painless and done carefully under general anaesthetic) is done on a young dog. You will still have the same loving pet, and if anything, they might be a little bit more calm for it!