What purpose does an attribute such as the spiked wheel of St. Catherine of Alexandria serve?

Explaination:

the stories about her, have been kept alive - and handed down in the tradition - certainly confirm her existence, and her life of heroic virtue and holiness.

The spiked wheel is a popular symbol often associated with St. Catherine.

Her feast day is Nov. 25, and she is the patron of a great many professions and causes. Her patronage includes students, unmarried girls, apologists and many more as well as many places around the world.