When I am publishing my site using Web Deploy in Visual Studio I see something like:
MySql.Data.MySqlClient is not supported for incremental database publishing.
I want to know what exactly would this technology do if it is supported?
Incremental database publishing is a deployment feature where the source code for the schema (new version) is compared with the live database schema (current version) to create a change script to upgrade the current version to the new version.
For example, if your schema has a table with a few columns and in the source code you add a new column definition, when publishing it would create a script to add the new column to the table.
It's not surprising that a database engine besides SQL Server isn't supported, since supporting other database engines would be a significant amount of work. All it really means is that you'll have to synchronize database changes yourself. MySQL may provide tools to help with this, but Visual Studio doesn't.