A SQL database is simply a database you read and write using the SQL language, storing data in structured tables that link to each other. In practice the phrase is just another name for a relational database, because both mean the same thing: tables, columns, relationships and the SQL language on top.
A handy way to picture it is a stack of well-organised spreadsheets that know about each other. One sheet holds products, another holds orders, and an order points at a product by its ID instead of copying every detail. The difference from a plain spreadsheet is that a SQL database enforces the rules, handles thousands of users at once and answers complex questions in milliseconds. Common examples include MySQL, PostgreSQL and SQL Server.
That rule-keeping is the quiet strength. A SQL database can refuse an order that points at a product that does not exist, or guarantee that a payment and the stock change either both happen or neither does. Those guarantees are why banks, shops and accounting tools lean on them: the data stays consistent even when many things happen at once.
You shape that structure up front by defining a schema, the list of tables and columns and how they connect. That bit of planning feels strict compared to just dumping data in, but it pays off later. Reports stay reliable, and a new developer can read the schema and understand how your business fits together in a few minutes.
The main alternative is NoSQL, which trades strict structure for flexibility and is handy when your data is loose or arrives in huge volumes. For most business applications with clearly related data, though, a SQL database remains the dependable default.
At TopDevs we run most client applications on a SQL database, because structured, consistent data is what keeps reporting accurate and the software easy to extend.