I want to use a database cursor; first I need to understand what its use and syntax are, and in which scenario we can use this in stored procedures? Are there different syntaxes for different versions of SQL Server?
When is it necessary to use?
Cursors are a mechanism to explicitly enumerate through the rows of a result set, rather than retrieving it as such.
However, while they may be more comfortable to use for programmers accustomed to writing While Not RS.EOF Do ..., they are typically a thing to be avoided within SQL Server stored procedures if at all possible -- if you can write a query without the use of cursors, you give the optimizer a much better chance to find a fast way to implement it.
In all honesty, I've never found a realistic use case for a cursor that couldn't be avoided, with the exception of a few administrative tasks such as looping over all indexes in the catalog and rebuilding them. I suppose they might have some uses in report generation or mail merges, but it's probably more efficient to do the cursor-like work in an application that talks to the database, letting the database engine do what it does best -- set manipulation.