Is { get; set; } useful?

Question

from time to time, I see some sample code that is handed to me that has a code snippet that looks like this:

public string Name { get; set; }

Does this actually do anything? Does it really make it so that one can set and get the "Name" string variable?

 

I have always thought that what is required is something like this:

private string name;

        public string Name
        {
            get
            {
                return this.name;
            }
            set
            {
                this.name = value;
            }
        }

Am I correct?

Please advise.