Avatars are essentially the user pictures that show up when you sign in. These are synchronized from the AD attribute or a server where the pics are stored. It's not mandatory but makes the user experience better.
If possible i would avoid Directory Connector now and just connect to Azure. No server to install.
Worth keeping in mind is that there are some caveats with the SCIM connection compared to Directory Connection, if memory serves me especially group synchronisation. So if you use that for licenses assignment you might want to hold off using the Azure synchronisation.