Based in is the single country where you are based. Active in lists the other countries where you are active.
Based in is one country: the country you are based in. You select a single Based in country on your profile.
Active in is a list of countries where you are active. You can select multiple Active in countries, or none at all.
Based in is required to save your profile, while Active in is optional. Recommended matching may use your geography, including your Based in and Active in countries, to show relevant Missions.