This question already has a good answer, but I want to supplement it with some more pictures. My full answer is here.
To help me remember frame, I think of a picture frame on a wall. Just like a picture can be moved anywhere on the wall, the coordinate system of a view's frame is the superview. (wall=superview, frame=view)
To help me remember bounds, I think of the bounds of a basketball court. The basketball is somewhere within the court just like the coordinate system of the view's bounds is within the view itself. (court=view, basketball/players=content inside the view)
Like the frame, view.center is also in the coordinates of the superview.
The yellow rectangle represents the view's frame. The green rectangle represents the view's bounds. The red dot in both images represents the origin of the frame or bounds within their coordinate systems.
Frame
origin = (0, 0)
width = 80
height = 130
Bounds
origin = (0, 0)
width = 80
height = 130
Frame
origin = (40, 60) // That is, x=40 and y=60
width = 80
height = 130
Bounds
origin = (0, 0)
width = 80
height = 130
Frame
origin = (20, 52) // These are just rough estimates.
width = 118
height = 187
Bounds
origin = (0, 0)
width = 80
height = 130
This is the same as example 2, except this time the whole content of the view is shown as it would look like if it weren't clipped to the bounds of the view.
Frame
origin = (40, 60)
width = 80
height = 130
Bounds
origin = (0, 0)
width = 80
height = 130
Frame
origin = (40, 60)
width = 80
height = 130
Bounds
origin = (280, 70)
width = 80
height = 130
Again, see here for my answer with more details.