I wonder why all Table Views (also in Android) have to have special object that provide them data ?
Why Table Views can't be populated from controllers (or Activity class in the case of Android) ?
For example UILabel in iOS can be populated just by setting "text" property
Could you explain what is the purpose of such design ?
This is a really great question.
We can break this into two reasons - a general one and a specific one that is a common example of it.
First, though, notice that it's even more than that. A UITableView can have two delegate controller objects, a UITableViewDataSourceDelegate and a UITableViewDelegate. The first provides the data; the second responds to actions taken on the displayed data. Why all these layers of abstraction? Why not just stick it in the UIViewController?
The general reason not to is suggested by the name 'UIViewController'. It's meant to control views. In iOS and I expect in android-land, there is a strong temptation to just 'stick it in the view controller' - leading to the Very Large View Controller antipattern, which you can read about a lot (eg here).
Far better for maintenance and organization for the view controller to lay out views and handle button presses, and some other controller object to handle the well-defined and really quite separate responsibility of providing the data.
It's not uncommon to have some sort of object that handles the data anyway - a shopping cart, or list of real estate properties, etc - that encapsulates additional business logic (providing subtotals, for example) but fundamentally already 'has' the data. In that case, provide a category or a lightweight controller that can 'bridge' between that data and the table view, and pass the model object, instead of an array, between view controllers.
This gets into the specific: in iOS, we have things like NSFetchedResultsController. This is a fantastic class that does a tremendous amount of data sorting, pagination, addition, deletion, slicing, dicing, folding, spindling, and mutilating for you - and it also speaks UITableView's language natively. Pass one of those around and you keep your view controllers clean and tidy and separate from your data.
TableViews do need a special or separate object but they do require an object implement the correct protocol so that it can find the data. In Apple's default implementation, it Uses a UTableViewCotnroller that is a new object responds to these methods as well as does some other things such as making the UITableView the root view of the view controller.
If you do not want to use that object for whatever reason you can still manually add a UITableView to your view controller, then sets its delegate to the view controller. Although it is a good to move it out of the view controller if possible to help keep the view controller small and the data reusable.
