What is the purpose of the "get" and "set" properties in C#

They are just accessors and mutators. That's how properties are implemented in C#

In C# 3 you can use auto-implemented properties like this:

public int MyProperty { get; set; }

This code is automatically translated by the compiler to code similar to the one you posted, with this code is easier to declare properties and they are ideal if you don't want to implement custom logic inside the set or get methods, you can even use a different accessor for the set method making the property immutable

public int MyProperty { get; private set; }

In the previous sample the MyProperty will be read only outside the class where it was declared, the only way to mutate it is by exposing a method to do it or just through the constructor of the class. This is useful when you want to control and make explicit the state change of your entity

When you want to add some logic to the properties then you need to write the properties manually implementing the get and set methods just like you posted:

Example implementing custom logic

private int myProperty;
public int MyProperty
{
   get
   {
       return this.myProperty;
   }
   set
   {
       if(this.myProperty <=5)
          throw new ArgumentOutOfRangeException("bad user");
       this.myProperty = value;
   }
}

It seems as though you understand the functionality of getters and setters, and others answered that question. "Normal" class variables (without getters and setters) are called "fields", and "properties" (which have the getters and setters) encapsulate fields.

The purpose of properties is to control outside access to fields. If you want a variable to be read-only to outside logic, you can omit the setters, like so:

private int dataID;

public int DataID {
    get { return dataID; }
}

You can also make the setter private and achieve the same read-only functionality.

If an object has a chance of being null (for whatever reason), you can guarantee an instance always exists like this:

private Object instance;

public Object Instance {
    get {
        if (instance == null)
            instance = new Object();
        return instance;
    }
}

Another use for properties is defining indexers.

//in class named DataSet

private List<int> members;

public int this[int index] {
    get { return members[index]; }
}

With that indexer defined, you can access an instance of DataSet like this:

int member = dataSet[3];

Check these links,.. they gives clear explanation.

http://www.dotnetperls.com/property

http://code.anjanesh.net/2008/02/property-getters-setters.html

if UserName and UserPwd are class variables, better to use like this

_userName 
_userPwd