'Miniature model' mode effect is derived from tilt and shift lenses.
With a 'normal' lens the plane of focus is parallel to the camera. As you turn the focus ring the plane of focus shifts backwards and forwards relative to the camera, but it always remains parallel. The first party trick of a tilt and shift lens is that you're able to change the angle of the front lens element relative to the camera (hence the 'tilt' part of the name). This causes the plane of focus to change angle too, so that it's no longer parallel to the camera.
'Converging verticals' is the odd effect of buildings appearing to fall backwards because the camera was tilted upwards to fit the building in.
This has one of two effects depending on which way the lens is tilted. Tilt it one way and you can throw more of a scene out of focus than would be possible by using the lens' maximum aperture. This produces a peculiar effect that's commonly referred to as the 'miniature model' effect; a perfectly normal scene looks as though it's actually a model diorama. It's such a striking effect that many cameras now feature it as an image processing option – though one that's usually not quite as effective as when achieved using a tilt and shift lens.
Shifting the front element of the lenses makes it easier to fit the subject into the image while still keeping the camera parallel.
More useful to the landscape photographer is what happens when the lens is tilted the other way. By careful tilting of the lens it's possible to increase apparent sharpness throughout the image without the need to use particularly small apertures. It's not that depth of field has increased, it's just that the plane of focus can be made to pass through the most important areas of the scene. This is known as the Scheimpflug Principle, named after someone called...well, Scheimpflug.
Canon use the prefix TS-E to denote their tilt and shift lenses.
The second party trick is that the front lens element can be moved up or down, left or right relative to the camera. Would it surprise you that this is what the 'shift' part of the name relates to? This is most useful when shooting architectural subjects. The camera can be kept parallel to the subject and the lens shifted so that the subject can be framed correctly within the image space.
Nikon use PC-E (for perspective control) to denote theirs.
Keeping the camera parallel to the subject avoids ‘converging verticals’. This is an odd effect caused when a camera is tilted to fit a vertical subject into an image. This results in the vertical lines of a subject no longer appearing parallel to each other: converging in other words. This often makes buildings look as though they're falling backwards, which isn't what any self-respecting architect would would want for his or her creation.
Tilt and shift lenses are made by both Canon and Nikon for their respective camera systems. As they're rather specialised they tend to be more expensive than equivalent prime lenses. A cheaper alternative is the new Samyang/Rokinon 24mm tilt and shift lens. This is available for both Canon and Nikon as well as Sony and Pentax cameras.