A SQL client is, as the name indicates, a client for a SQL Relational Database Management System (RDBMS). It can help you manage (create, read, modify/update, delete) DBs.
Some kind of administration tool is available with each RDBMS (you could have it installed on your computer or only on the server). But sometimes you'll have productivity gains if you use a multi-DB client because using the same SW user interface you will be managing several different DB engines / instances.
Examples of DB Tools include: Aqua Data Studio (Windows, proprietary - this one scripts data into DML SQL statements), Squirrel SQL Client (open source, java-based).
A comparison of DB tools can be found - where else? - in Wikipedia so choose one according to your requirements (and that might be shaped by your budget):
https://en.wikipedia.org/wiki/Comparison_of_database_tools
For SQL Server, as per 2016-11:
SQL Server Management Studio (SSMS)
https://msdn.microsoft.com/en-us/library/mt238290.aspx
SQL Server Management Studio Express
https://technet.microsoft.com/en-us/library/ms365247(v=sql.105).aspx
And a related download - SQL Server 2016 Express (the free DB engine):
https://www.microsoft.com/en-us/download/details.aspx?id=52679
(Updates: @2016-11-08: MS SQL Server example links)
