What does it mean that a gene exhibits codominance?

Essentially traits of both genes will be shown. Take heterochromia for example, where a person has a green eye and a blue eye, both have some part in developing a trait.

I answered a similar question before so I'm going to use an example from there. Two plants, a dark purple flower and a white flower create an offspring with dark purple and white petals on the flower. This is an example of the gene displaying codominance in effect. 

Codominance allows for two genes to exist independently at the same time without mixing. Think of another example. Say your mother has blue hair and your dad has red hair. If you have both blue and red strands. That is codominance. The two colors who co-exist. If you got purple, you would have incomplete dominance. Notice that the purple is a mix and of blue and red. They are dependent on each other. 

Hope that helps! :D