My neighbor collects stamps. I don't really understand why.
Stamp collecting is considered a hobby to some. It has been popular since the late 19th century. 
That is a long time!
Stamp collecting is fairly easy also. There are always new stamps being created. Each country used stamps to differentiate from each others.
It sounds kinda interesting. Do people just collect stamps from different places they visit?
Sure. They also trade with others. Stamp collecting collect purely for the enjoyment and relaxation. The casual collectors do not worry about the small details.