App Store Optimization is the process of improving the app visibility in app stores (Apple Store & Google Play Store) so that the app is more often found by users and the number of downloads increases.
ASO is important because it brings you free organic downloads from users who are browsing the app store with SEO or searching for specific words within the app store.
App Store Optimization is often referred to as SEO for apps. This analogy comes in pretty handy when understanding the overall principle of ASO. But the app stores and the web are two very different ecosystems!