It can be useful for lazy-loading. Say the object in question is stored in a database, and you don't want to go get it unless you need it. If the object is retrieved by a getter, then the internal object can be null until somebody asks for it, then you can go get it on the first call to the getter.
I had a base page class in a project that was handed to me that was loading some data from a couple different web service calls, but the data in those web service calls wasn't always used in all child pages. Web services, for all of the benefits, pioneer new definitions of "slow", so you don't want to make a web service call if you don't have to.
I moved from public fields to getters, and now the getters check the cache, and if it's not there call the web service. So with a little wrapping, a lot of web service calls were prevented.
So the getter saves me from trying to figure out, on each child page, what I will need. If I need it, I call the getter, and it goes to find it for me if I don't already have it.
protected YourType _yourName = null; public YourType YourName{ get { if (_yourName == null) { _yourName = new YourType(); return _yourName; } } }