A database is a structured, organized collection of data stored and accessed electronically, typically in a database management system, such as MySQL or Microsoft Access. Databases can contain any type of data, including patient records, scientific observations, transcripts, maps, or historical records. They are structured so they can be easily expanded or updated to include new data, as well as to facilitate searching for and retrieving data.
There are different types of database structures (e.g., object-oriented, hierarchical), but the most common one is a relational database (e.g., MySQL, Oracle). In a relational database, data is stored in different tables (e.g., books, publishers, authors) that are linked to represent the types of relationships between the tables (e.g., a book can have many authors, a book can have only one publisher, an author can have many books). These tables and the relationships between them represent a data model. Retrieval from these databases is typically done using structured query language (SQL) for communicating within the system or an Application Program Interface (API) for communicating from another system. Another increasingly popular type of database is a NoSQL database (e.g., MongoDB) which does not store data in relational tables.
While databases can be created and accessed on individual computers, they are typically stored on network servers so users can access them remotely via the internet.
Two familiar examples of databases in the biomedical realm are PubMed, which stores metadata about journal articles, and EHR systems, which store data about patients.
Oracle provides a succinct overview of databases, including a definition, a list of database types, and common challenges associated with databases: https://www.oracle.com/database/what-is-database/