Q:

draw view in context, what does it mean?

I've got the view presented like this:
_myController = [[MSCustomViewController alloc] init];
    _myController.doc = (AWDOC *)_currentDocumentViewController.activeFile.document;
    _myController.view.backgroundColor = [UIColor colorWithHue:0.7/3.3 saturation:0.2 brightness:1.0 alpha:1.0];
    [self.view insertSubview:_myController.view aboveSubview:_myController];
    CGSize size = [_myController.view sizeThatFits:CGSizeZero];
    if(size.height < _myController.frame.size.height)
        size.height = _myController.frame.size.height;
    CGRect myFrame = CGRectMake(0., CGRectGetMinY(_currentDocumentViewController.view.bounds) + (CGRectGetHeight(_currentDocumentViewController.view.bounds) - size.height) / 2., size.width, size.height);
    _myController.view.frame = myFrame;
    CGRect buttonFrame = CGRectMake(CGRectGetMaxX(myFrame), CGRectGetMinY(myFrame), myButton.frame.size.width, CGRectGetHeight(myFrame));
    _myButton.frame = buttonFrame;
    [_myButton setTitle:@"<" forState:UIControlStateNormal];

What does mean "draw this view with context or Draw"?

A:

To add default UIView to your viewcontroller to hold the built-in views like UIButton,UIImageView,UILabel.You add as:
UIView *view = [[[UIView alloc] initwithFrame:CGRectMake(..)];

Now, to make the custom drawings in the UIView, you have to define your own view ( you do this by creating new class inheriting UIView). Let's say the class you made is StandardView class.
When you inherit the UIView, drawRect: is the default method which is called when you initialize this uiview in your view controller:
Standardview * stndView = [[Standardview alloc]initWithFrame:CGRectMake(0, 0, 320, 300];

So, you can place all your drawing stuffs inside your drawRect: method. Normally you do drawing either using OpenGL/ES or CoreGraphics. And when using the coregraphics functions you specify the context for every function of coregraphics.And that context means your graphic destination.

