App store is a marketplace for digital content. The Apps being applications or software. The most popular electronic marketplaces provide per-fee and free movies, music, games, books, magazines, in addition to software like Microsoft Word or Google Chrome. In the days of dial-up internet, known computer servers were hosting libraries of content accessible to all. What we have today are billion dollar websites geared toward mobile smartphone users.
The most popular are the Apple AppStore, Google Play, and the Amazon Appstore. Microsoft has an online app store but it not the most popular. In Linux, each distro will have a marketplace or repository of computer software.