Break it down:
public Class1()
{
}
Declares a constructor for a class created by an amateur - anyone with more than 2 grammes of experience would have given it a name which reflects what it actually does rather than leave the VS default name.
con = ...
Assigns a value to a variable, called "con" which from context is a class level variable, from the name it should be a private field.
... = new SqlConnection();
Says that the variable being assigned to is of the class SQLConnection (because SqlConnection is a sealed class, so "con" cannot have been derived from it, and it is unlikely that you would use anything lower in the inheritance chain to store an SqlConnection)
...ConfigurationManager.ConnectionStrings["connectionstring"].ConnectionString...
Gets the connection string for a database from the application default configuration.
Easy isn't it?
Next time, try that yourself, and if you don't understand a part of it, google!