Chromatography works by providing two environments for analytes to interact with. One environment is stationary and the other is mobile. The difference in the interaction of the analyte with the two environments determines how fast the analyte will move, and if two analytes have differing interactions with the two environments, they will move at different speeds. Since they are put on the column at the same time, they will come off at different times, and thus be separated.
In the case of chiral chromatography, your two environments are a specific chiral environment (in your case, cyclodextrin) and an achiral environment (your solvent system). Being enantiomers, your two components will have identical interactions with the achiral environment. However, if you have chosen an appropriate chiral environment, they will have subtly different interactions with that environment. One enantiomer will interact better with the cyclodextrin and be held on the column longer, while the other will not interact as well and will leave the column sooner. Imagine walking through a hall full of people where everybody is holding out their dominant hand for you to shake with your dominant hand - if you are right-handed, you're going to be shaking a lot of hands and moving slowly through the hall, while if you are left-handed, you'll only find a few hands to shake and will be able to move much faster.
Although you are not using a Pirkle column, you might want to read some of William Pirkle's early work on developing those columns. He did an excellent job of describing the interactions between the chiral stationary phase and the chiral analytes he thought were important in separating mixtures, and showing how that directed his synthesis of chiral stationary phases.