After a long battle between Ash, Misty, Brock, and Team Rocket for a enormous egg, Misty beat Ash out of the way, and got Togepi to look at her first. Togepi started following her around, forcing Misty to take care of it.
It was inherently lazy, forcing the gang to carry it everywhere, point-blankly refusing to say or do anything, when left to its own devices. Occasionally it likes to roll places. It gets into lots of bother and likes to make a general annoyance of itself. It waves its arms in case of danger.
Since Misty doesn't let anyone look at it closely, we must assume that there was something unusual about the pair.
In the beginning of season five, Togepi evolves into Togetic, due to an assassination attempt. It then ditches Misty and stays in the Mirage Kingdom forever with as horde of Togepi that somehow appear there. Misty always will miss her egg friend.