To get closer to us. They are excited and jump so that they can get our attention. Some dogs also have to use their teeth with little excited nips or sleeve grabs, but this is not aggression, it is over arousal. Most dogs learn during their puppy stage that jumping and biting is not acceptable, but if they miss out on vital training and you have a bigger dog it can become a real problem.
In Ollie's example here, he is struggling to find a home because every time a potential adopter goes to visit they get completely mauled in his frenzied excitement!
First we have to teach the dog what we do want him to do instead. In Ollie's case he has a really good "sit" so this is a good starting place for him. So he gets no attention unless he is sitting. Then we need to be completely consistent about never accidentally rewarding him for jumping up. So lots of praise and stroking for sitting nicely. The instant he goes to nibble a sleeve or jumps up then you stand up, pull in your hands and ignore him. Wait for the "sit" and hit repeat.
NB Don't make the mistake of shouting NO or waving arms around as this can cause even more excitement, or if you are too aggressive you can even cause your dog to become fearful of strangers.