A File Geodatabase (FGDB) is Esri's native data store for ArcGIS, implemented as a folder with a .gdb extension that holds multiple feature classes, raster datasets, tables, topologies, and feature datasets in a set of internal binary files.
Why it matters
It removes the limits of the shapefile. A File Geodatabase supports field names longer than 10 characters, preserves nulls, stores curves and rich attribute types, and handles datasets far larger than the shapefile's practical 2 GB-per-file ceiling (each FGDB table can hold up to 1 TB by default). It also lets related layers — geological units, faults, boreholes — live together in one container with consistent CRS and domains, which keeps a project tidy.
A concrete example
A geological mapping project might keep a bedrock_geology polygon feature class, a faults line feature class, and a boreholes point feature class inside a single project.gdb, all grouped in one feature dataset sharing EPSG:32631. QGIS and GDAL can read FGDB through the OpenFileGDB driver; writing is more limited outside ArcGIS.
Common pitfall
The FGDB is not the older Personal Geodatabase (a single Access .mdb file, now deprecated) nor the multi-user Enterprise Geodatabase (backed by PostgreSQL, SQL Server, etc.). It is also proprietary: full read/write support lives in Esri tools, so for cross-platform open workflows a GeoPackage is often the better choice. Never edit the files inside a .gdb folder directly — treat the folder as a single dataset.