A Live connection creates a direct link between the Tableau Data Source and the database (server or file). It means that, if the data changes, you see the impact in Tableau directly after refreshing the Data Source, or when you reopen the Workbook. 

The problem with a Live connection is that you are dependent on the performance of the database. Large text files, big Excel files, or an unoptimized database can be very slow to analyze in Tableau. Also, if you are connected to an online database, you are dependent on the internet connection, and you won't be able to work offline.

For these reasons, I advise you to always work with an Extract.