So here is one of THOSE topics among horse people in which for every person you ask you may get a different answer. I am going to give you my thoughts on spurs.
What are they for?
Spurs are used for refining the aids, particularly when you start getting into lateral movements for me, this usually second level-y. If you wait until the horse is too far along, it may be shocking to them when you decide to put them on to start schooling Grand Prix! The horse must also accept the spur and make an appropriate response.
Does every horse need a spur?
Nope. Not even close.
What are they not for?
Spurs are not for going forward (remember forward is a direction). They are not for speed, or tempo. The horse should know to go forward from the leg well before you would introduce spurs. That is the place that spurs have the potential to be abused the most, when a rider is kicking their horse to go forward. Using your spur to get a dull horse going forward can make the horse even more dull. If you need help getting your going forward properly, check out 30 Days to a More Responsive Horse.
Who are they for?
Riders with an independent seat that can distinguish between the toe pointed forward and flat of the inside calf on the horse and the toes out where the spur can touch the horse.
In summary, spurs are for qualified riders to refine their aids even further. Any tool can be abused and it does happen with spurs. They can also be used very well. Proceed with caution and listen to your horse.
As always, enjoy the dance!