Extract connection is a connection to a static database that is updated every day / hour / period. The data is copied from the data source to the Tableau Server. Refreshing the data source doesn't give you the latest
data-you need to refresh the extract to get it.
Live connection will check the underlying data in the datasource / database-the latest results will be provided by refreshing the visualisation. No preprocessing data is copied to Tableau Server.
Check out tableau training that enables you to master your skills in BI