Scalar user-defined functions in SAP HANA allow users to define functions that take scalar input parameters and return scalar values. They can be used like built-in functions in SELECT statements. The basic syntax to define a scalar UDF includes specifying the input parameters, return type, and function body. For example, a function was created to convert hours to minutes by multiplying the input hours by 60 in the function body. This UDF was then called in a SELECT statement on a table to return overtime hours in minutes.