What an ATS does
An ATS pulls together, in one place, the open roles, the candidates who apply, and where each one stands in the process: applied, interview, offer, hired.
Who needs one
If you run fewer than 3 openings a year, a spreadsheet is probably enough. If recruiting is central to the business, an agency or a corporate TA team, the volume of simultaneous processes makes a spreadsheet fall apart.
ATS vs. spreadsheet
A spreadsheet does not send reminders, does not screen CVs, and desyncs the moment two people edit it at once. An ATS fixes that, and adds a history per candidate that a sheet never keeps.