Microsoft InfoPath is a piece of software that Microsoft sells. InfoPath is used to create computer-ized versions of documents people have to fill out.
InfoPath has two main parts: an 'editor' interface, used to make and design forms, and a 'form-filling' interface, used to fill out forms that have been made in InfoPath. For example, if someone had to fill out a timesheet on a regular basis, they could use InfoPath's editor to replicate the timesheet form. Every time they had to fill out the timesheet, they could open the form they made in InfoPath, fill it out using InfoPath's form-fill interface, and then save it as a file for archival and print it out if they ever needed to.
Forms that have been made in InfoPath can be put on SharePoint websites. Forms can also be amended with XPath, Basic, or C# computer code to do mathematics or read from and write to databases.