Getting Started
I mentioned that green is a safe colour. Just like a traffic light means "GO" many games start off with a "green" level to ease the player in. Take a look at these examples:
Sonic Green Hill Zone
(first level in the first Sonic game)
Little Big Planet Garden
(This game is fairly different from most games even in its genre, it starts off in a simple garden)

The Legend of Zelda: Ocarnia of Time
(The first 3d Zelda game opens up in a happy green village, Kokiri Forrest)

Halo: Combat Evolved
(Second level in the game but the first real open long level)
Of course not all games start off green but many do. Even if the first level isn't green at least one of the earlier levels are. Its very common to start a game in a forest themed level. The imagery of nature not only uses this colour but since it is set in a recognizable setting the player feels more at home. Many people have been to a forest but not many people have gone through lava or a dangerous tundra. Thats why the lava levels and ice levels usually appear later in a game. It all goes back to that basic instinct, "Green Means Go." If you start a game in a red firey level you are telling the player that this game is going to punish you from the get go. Starting the game with an easy green level lets the player get accustomed to the game before moving on to the harder stuff.
The HUB
Many open world games (games without real level progression) cannot directly lead a player level by level. So most of these games have the hub area, an open space you adventure across to access different parts of the game. These hubs are almost always green. Hub levels need to be safe and welcoming. The player needs a break from the harder parts of the game and moving across the green hub can let them calm down and recollect. Here are some examples of how the green hub helps this way:

Zelda Hyrule field
(There are some enemies on the field but they are very easy. Transversing Hyrule field is a much needed break from the difficult dungeons).
Oblivion
(The game starts in a dark dungeon but after that short intro you walk out and are welcomed by green. Most of the hard battles are done in dark caves of eerie dungeons. Every time you finish those parts of the game it is a nice break to enjoy the open world.)
Final Fantasy
This is one example but basically every RPG's world map is full of vast open green fields. There are some random encounters on the world map but they are never as difficult as those found in the dungeons.
Shadow of the Colossus
This game is mostly about riding your horse through open nature. You go through these forests and fields in order to find the giant bosses. These fields are the only completely safe parts of the game.
Super Mario 64
When this game came out it was the first of its kind. No one had really made a 3D platformer of this magnitude. The player had to get used to a completely different control system. The game started off in a safe castle garden for you to learn in.
That is what the colour green means to video games and how it contributes to the visual aspects of the art. Green is the quintessential safe colour, and can easily welcome players into the video games world. These are the main reasons my blog's is colour scheme is based on green.