Zapier lets you connect various applications together. It basically builds connectors for each application which can then be linked to perform certain tasks like sending a mail in Gmail to a Google spreadsheet.
Zapier relies on each underlying application to expose an API. For every task it can perform it needs an underlying API or connection from the App. For example Gmail gives an API to read any mail that comes to your account (if authorized). Similarly, Google spreadsheet gives an API to add a row to a given spreadsheet. Together these can be connected to add a row to a spreadsheet whenever a certain email comes. Zapier allows you to easily make these connections and thereby automate some tasks across products.
Zapier does have a free tier plan which allows you to make certain connections which can be called a certain number of times in a month. Beyond this quota it requires paid plans.