A relational database is a way of storing data in connected tables (entities) that have relationships between them - instead of isolated sheets, the way a spreadsheet works. A client record links to the jobs the company does for them, and those link on to invoices or tasks, without the client's details ever needing to be retyped anywhere.
The main advantage over a spreadsheet file is consistency: when a client's phone number changes in one place, it shows up everywhere that client is used - in jobs, invoices and communication history. In a spreadsheet, that change would need to be repeated manually in every sheet, which is exactly where mistakes and mismatches creep in.
A relational database is the foundation most business systems are built on - CRM, ERP, project management - because it can model the real relationships between clients, jobs, invoices and people.
Related: When a spreadsheet stops being enough, A data model that grows with the team, Databases and relations.