Webmaster Tools is the old name of Google free application that allows webmasters to view data about how Google's search bots see their website. Google Webmaster Tools is now called 'Search Console', but Bing still call their application 'Bing Webmaster Tools'.
The Search Console is a fantastic resource for helping SEOs to optimise their website, particularly from a technical standpoint, as the data about how Google crawls and displays their website is in-depth and straight from the horses mouth.
The accuracy of data in the Search Console has come under question a few times and shouldn't be wholly relied on without using other tools to backup and cross check any conclusions that you draw. Search Console also only reveals data for the last 90 days, with a three day lag, so analysing trends over longer periods or for the present can be difficult.