There is a broken abstraction in traditional Objective-C, which is the accessor-method-as-property-declaration. Essentially an object can give you two things; work (i.e. it can do stuff) and state information (i.e. it can say stuff about itself and let you change it). In traditional object-oriented languages, because 'saying' and 'changing' are verbs which can be 'done', the two have both been expressed using the same method (heh) as the expression of work. This is not the case in much object-oriented design, for instance in UML a class always has separate "attributes" and "operations".
Properties fix up this abstraction by giving us orthogonal ways to express the two concepts. Work is done in methods; state is got/changed in properties. Now it may be that the state information is actually backed by a method (although it may bang on the ivar directly; more below), but we don't need to know that any more than we need to know in the interface that a property is synthesized or dynamic. All we do need to know is that it is there for us to use, and has certain attributes such as being read-only.
The "on more below" bit is that discussions of KVC-like mechanisms - such as KVC :-) - often involve someone pointing out that they break encapsulation, because it's possible to access an @private ivar with no accessors by retrieving it by key. That's really thinking about the design of a class in terms of the way it's executed rather than its interface contract with the developer, because the @private ought to tell the developer not to touch that particular ivar. Properties neither help nor hinder breakage from the execution side, but from the design side they do provide a stronger distinction between "properties I'm telling you about in the interface" and "things you shouldn't touch". Now we can all get back to using the class's interface to observe how to use it, and that C struct bit at the top to observe how to extend it, as nature intended. It's both a blessing and a curse that Objective-C allows things to appear in source files which don't make it into the executable code, but that doesn't stop such information being useful to the developer in the same way that code comments can be read but not executed.
One of the popular complaints about ObjC properties is the syntax for referring to them in methods (OK, or indeed in functions), where it is argued that myObject.someProperty = 4; doesn't readily tell you whether myObject is an ObjC object, a C struct or a C union. That seems to be at worst a straw man argument to me, and at best a hypothetical issue; in well-designed software it will be rare to mix code at various levels of abstraction except in limited circumstances such as adapter classes. Besides, if the code has been written such that it can be inspected or reviewed (i.e. to some agreed style and standard) and the reviewer is paying attention then it will be easy to distinguish use of the various types. At some conceptual level the C . and Objective-C . operator are doing the same thing anyway; they're both saying "this attribute of that thing".
[*]The fact that I have stopped using the word 'feature' in many contexts is an entire blog post and a few therapy sessions in itself.