Inactive ingredients (technically called "excipients") in supplements, which are listed as "Other Ingredients" on supplement labels, are used to help stabilize ingredients and increase shelf life, improve consistency, improve resistance to moisture, hold tablets together, add bulk (facilitating manufacturing with small amounts of key ingredient), add color, or add flavor.
These ingredients are regulated by the FDA as food additives and are generally considered to be safe in the small quantities used in dietary supplements. However, some ingredients, such as certain coloring agents, may cause allergic reactions in sensitive individuals. For details about the various inactive ingredients found in supplements, the reason for their use, and safety, see the Review Article on Inactive Ingredients >>
If you want to avoid certain inactive ingredients, ConsumerLab.com publishes the full list of these for every product it reviews. Just check the "Ingredients" page associated with each Product Review