Random files are record-based files with an internal structure that supports "direct access" by record number. This means that your program can read from or write to a specific record in a random access file, say the 50th record, without reading through the previous 49 records. Compare that to reading or writing a sequential file, where to get to a specific record, you must read through all preceding records.

 The difference between random access and sequential access can be likened to accessing music on a CD versus a cassette tape. To get to song number 6, you can tell your CD player to go directly to track 6, whereas on a cassette tape, you must fast-forward through the first 5 songs to get to song number 6.

In the earlier days of BASIC, before the "client-server era" where RAD systems such as VB, Delphi, and PowerBuilder interacted with desktop and ODBC databases such as MS-Access, SQL Server, and Oracle, random access files were used as building blocks to put together data access systems that could be considered early forms of desktop databases.