please explain me this code.

public partial class _Default: System.Web.UI.Page

Defines one class named _Default that inherits from System.Web.UI.Page. The partial keyword instructs the compiler to not generate errors for not finding at this scope the entire declarations and definitions for the class _Default. The rest of the class should be provided in another similar declaration (using the partial keyword also).

private static readonly string _connString = String.Empty;

Declares one private (scoped to the class, invisible out of there) field which can not be written (that's the meaning of readonly). The static keyword specifies that this field will be global (shared by) to all instances of that class.
Code writing to static fields is not reentrant, take care with that.
One thing else, the fact that it is marked readonly implies that it can not be changed, so it makes no sense to initialize it with the value String.Empty if it will be used later like your code does.

SqlConnection con = new SqlConnection(_connString);

This creates one instance of the class SqlConnection(). Take a look at this, as _connString can not be modified and has been initialized with an empty string... presumably you'll not be able to establish the connection with this code.

Perhaps you should consider removing static and readonly from your _connString declaration.