Where an app keeps information
An online shop needs to remember customers and orders. A database keeps that information organised so the shop can find a customer or update an order. Many databases arrange it in tables, like spreadsheets: each customer has a row, with columns for details such as name and email address.
The main database for an online service usually runs on a server. Some apps also keep a smaller one on a phone or computer so they can work offline.
Organising and protecting the records
Databases can use different layouts. Some link tables of customers and orders; others keep complete records as documents. These are among the approaches described as SQL and NoSQL.
Whatever the layout, the team still decides who can use the data, checks that entries make sense, and keeps backups. A database does not do those jobs by itself.