LocalDB was first introduced with the CTP3 version of SQL Server 2012. Basically, it is a newer version of SQL Server Express, which has the same characteristics in terms of functionality, but it is mostly dedicated to developers.
It does not require you to install any SQL server. If you have installed SQL 2012 or Visual Studio 11 or higher then you already have LocalDB. Also, it runs only on .Net 4.0 and higher.
How to connect to MS SQL LocalDb
You can connect to a named instance of SqlLocalDB with SQLBackupAndFTP just by entering the string (LocalDB)\<instance-name> into “SQL Server Name” at the SQL Server section.
Where <instance-name> is your named instance of SQL LocalDB.