In Software Engineering, Front End & Back End refer to the Presentation Layer & Data Access Layer, respectively.
Data Access Layer is a layer of Computer program which provides access to data stored in persistent storage. ie entity-relational database.
In Computer Science, Persistence refers to the state that outlives the process that made it. ie This happens by storing the state as data in storage. Specific examples: Paint, Microsoft Word, have a state persistence by saving their documents to files.
Conjecture: While you are using Microsoft Word, note that the software periodically auto-saves your progress. This data persists for recovery in the event of an error or crash.
The Front end is the interface (GUI, LUI) between the user and the back end. i.e. Windows 10.
Summery: Front end is for client. Back end resides on server.