In C#, what makes a field different from a property, and when should a field be used instead of a property?
Properties expose fields. Fields should (almost always) be kept private to a class and accessed via get and set properties. Properties provide a level of abstraction allowing you to change the fields while not affecting the external way they are accessed by the things that use your class.
public class MyClass
// this is a field. It is private to your class and stores the actual data.
private string _myField;
// this is a property. When you access it uses the underlying field, but only exposes
// the contract that will not be affected by the underlying field
public string MyProperty
_myField = value;
@Kent points out that Properties are not required to encapsulate fields, they could do a calculation on other fields, or serve other purposes.
@GSS points out that you can also do other logic, such as validation, when a property is accessed, another useful feature.