A formula is a calculation the database runs automatically from values in other fields - similar to a spreadsheet, except in a database app you write the formula once on the entity and it then applies to every record in it, instead of to every cell separately.
A formula can work with values on the same record (price excluding VAT × VAT rate = price including VAT) or with values from related records through a relation - for example, a job's margin can be calculated from the invoiced amount minus hours worked times the hourly rate, even though those figures live on other entities.
The advantage over a spreadsheet is that a formula stays valid even after a new record is added - it doesn't need to be copied down to the next row, and there's no risk that one sheet keeps a stale formula while another has already been fixed.
Related: Reporting via view columns and formulas, The agency that knows what it actually earned on every job, What is an aggregation (rollup).