While new games did not always come with considerable graphical leaps, they did surprise users with the number of features they could now offer. This was thanks to the new services Nintendo shipped with the console's launch, ranging from the new set of controls, to a standardised online infrastructure (WiiConnect24) which enabled free online gaming.
Medium
Wii games are distributed using a proprietary disc format called Wii Optical Disc (I know, the name can't get more obvious). Anyhow, Matsushita/Panasonic designed this format based on the traditional DVD disc while adding non-standard features, like a burst cutting area on the inner section of the disc to prevent unauthorised reproductions.

Standard games are presented in a physical box and disc.

Small games (WiiWare) and emulated games (Virtual console) can be purchased and downloaded through the Shop Channel.
The Wii disc provides either 4.7 GB (if single-layer) or 8.54 GB (if double-layer) of space available. They often contain two partitions: The first one for system updates and the other one for the actual game.
Some games like Super Smash Bros. Brawl included more partitions to store multiple Virtual Console games, which were executed inside the main game.
Development
As part of the tradition, Nintendo supplied a development kit. This one was called NDEV and shaped like an enlarged black brick. NDEV shipped with enhanced I/O and two times the amount of MEM2 (128 MB in total) for debugging purposes.
The official software suite was named Revolution SDK and it included various tools, compilers, debuggers and frameworks to carry out development (mostly in C/C++). Nintendo distributed subsequent updates through a web portal called Warioworld.com (now offline/redirected) which only approved developers could access.
The official SDK relies on IOS calls to interact with the Wii hardware, this is why IOS updates are often correlated to SDK updates.
Return to Home
Considering all the software advancements of this console, it may surprise you that games still run on bare metal, which means that they have complete control of Broadway, but not of Starlet (hence, security mechanisms are implemented here). Needless to say, the game's behaviour is still subject to Nintendo's approval before getting distributed.

This screen has to be included as well.
Having said that, there are certain features across different games that look awfully identical, somehow. For instance, do you remember the famous HOME Menu? Pressing the 'HOME' button on the Wiimote will trigger a screen popup in-game, enabling the user to return to the System menu without the need to reboot the console. Considering the OS does not provide this feature, how did every single game manage to come up with the same graphical interface?
The answer is simple, Nintendo included in their SDK some mandatory libraries that games have to embed. Lo and behold, one of them draws that screen. Furthermore, this is the reason you'll find that only homebrew apps feature 'original' designs for the home menu.
The official HOME Menu is one of the 200 or so requirements games had to include, as ruled by the Wii Programming Guidelines document (found on the official SDK). Other requirements consisted of displaying the 'Wii Strap reminder' screen (which is just a BMP image) at the start of the game, followed by another rule that dictated how to interact with it.
Personalised titles

The Mii channel allows to fiddle with your own 'Mii'...

...which then appears in your games.
Wii Music (2008).
Another new feature I would like to emphasise is the introduction of Miis, some sort of avatars that users could create using a dedicated channel called Mii Channel.
But the fun didn't stop there, since games could also fetch these new-created Miis to personalise gameplay.
