"Spikes" is the general term that refers to a Track shoe which has 6 spikes at the toe end of the shoe.You do not have to have spikes to compete on the track. Flat running shoes are fine.
But, if you are serious about competing you might want to consider getting some track shoes with spikes in them which help to grip the track in Summer (6mm) or grip the grass in Winter (12mm). Talk to your local sports shoe shop about whether to get a general purpose shoe or event specific such as harrier, sprint, middle distance or a jump shoe.