These are the bread and butter of pretty much every game now. These define the sounds your enemies and players will make in the world, the environmental reactions to your actions. This ranges from things such as character footsteps, sword slashes, gunshots, explosions and anything that is resulted from an action or visual change in the environment. It can be a scripted sequence like a bomb going off and setting off that explosion, or your character holding a gun and you, the player making the gun shoot by pressing the trigger.
The reason these are so important is because they are something you will hear a lot during your game, pretty much all the time. It means that they cannot be annoying, tedious or repetitive. They need to be designed in such a way that they make the experience for the player even better. They need to be satisfying and make sense with what's happening on screen.
Bioshock - They use an excellent opening that uses a perfect mix of visuals and sounds
Something satisfying would be the gold drop sound in Diablo 2. You hear that sound and immediately know that gold is somewhere to be picked up. The sound is kind of addicting and makes you want to go pick it up immediately because it has this satisfying feel to it. Diablo 2 also makes it so different items would make different sounds too, so if a potion drops, it makes a distinct sound, same with a large weapon or a small weapon. These sounds are both satisfying to hear and provide us information, even if it's not fully on screen yet.
Diablo 2 - A few iconic sounds, potion, town portal sound and going through the town portal
A game that had you shooting a gun but fired what sounded like pellets would be very unsatisfying. If the tool you're using is making sounds that don't naturally fit it, it will take you out of the game. It won't feel right and as a result probably won't be satisfying either. A problem with this is that games can also be subjective in terms of sound and what they should sound like.
For example, the average Call of Duty player doesn't really know what guns really sound like. A trained ear in gun sounds can detect a lot of inaccuracies with Call of Duty's gun noises which detracts the experience for that player. For the others though they don't even know and might think they are accurate anyways. Battlefield: Bad Company 2 and Battlefield 3 on the otherhand have been praised for their accurate sound effects that really help immerse you in the game. Also Call of Duty has reused sound effects a lot for their guns.
Battlefield 3 & Modern Warfare 3 Sound Comparison
Ambiance would be defined as sound that is only meant to enhance the experience. It's in the background, very faint and subtle that's designed to ease the player in or out of the experience. It's not as obvious as sound effects which are more about giving feedback about what your actions are in the game. A good example of what ambiance is would be birds chirping in the background of the environment in Skyrim. Another would be cricket sounds or slight distortion noises in a game like Slender.
The reason ambiance helps so much is that it makes the world feel alive. When you're not performing any major actions, just exploring the environment or even just standing still, if you just hear complete silence its usually not a good sign, (depending on the game of course). Imagine you're in an environment where gears are rotating around like some sort of clockwork tower. You certainly wouldn't hear silence that's for sure but you also wouldn't want to hear the cranking of gears constantly as it would irritate the ears. The ambiance would be for some subtle clock sounds in the background, not too loud but not too quiet. It would be a balance in between that helps reinforce the environment you're in.
The same with a game like Slender. There is no music and the only sound is your footsteps or a thumping noise from Slenderman every now and then. The rest of the sound is crickets and other bugs in the distance. It helps add to the experience that you're in an actual forest, and in a horror game atmosphere is everything. Absolute silence in the ambiance wouldn't work quite as well as the environment might not seem as natural and therefore take you out even more.
Slender - Playthrough (Just listen for the ambient noise)
Going back to Skyrim again, the use of ambient noise in the outdoor environments is subtle and you might not even notice at first but it's there. The reason you don't notice is because it helps sell the environment so well that you just feel apart of it already. If there was absolute silence in the ambiant however, you would definetely notice it. It would feel off because there are always other sounds in nature, at least some. There is hardly ever complete silence.
Though I haven't posted my Tunes of the Week blog in some time, I have not neglected how important music is in games. I've already gone on several blogs about this topic already so I don't want to cover this too much. But reiterating briefly...
Music is important in games because it helps define the experience and helps define the memories for us. Familiar catchy tunes help us to both progress in the game and help us remember those experiences later. Whenever you hear the Super Mario theme, it's very sound can reinvoke memories inside of you because of it's association with the game. The fact that the tune is so catchy also makes it so it comes back to you and might make you want to play more.
Bayonetta - You may Call me Father (From the 2nd last Boss battle)
Music can help drive a lot of players to play again depending on their tastes. I myself have played certain boss battles in games over and over because of just how spectacular the experience was, from gameplay to the music, sometimes even just for the music. Other times I stay in certain areas because the background music is simply so catchy, or beautiful depending on the game.
Halo 2 - Blow me Away (From the level "Gravemind")
For example I played the two final levels of Bayonetta over and over because the music and entire boss fight was just so spectacular. I replayed the level "Gravemind" in Halo 2 over and over because at the end of that level, it had some really badass music. I roamed the fields of Hyrule in Zelda: Twilight Princess because I just enjoyed the background music. I've done all of these actions for no other reason then the music sometimes and that to me goes to show the music has done it's job.
Legend of Zelda: Twilight Princess - Hyrule Field Theme (Played in Hyrule Field)
Finally, sometimes it's just a final, beautiful reward for beating some games.
This is the one area that can be debatable. In fact, I believe it's best to save this one to it's own blog post as there are a lot of variables with how dialogue can effect the game or not even be required in one. A quick overview of what would be in store for the future is Zelda vs Final Fantasy. Dialogue driven they both are, but one contains actual dialogue while the other is simply reading.
FOR LATER THOUGH.
To me, sounds are really one of the most important parts of games. I used to play some games without sound because of various reasons (like a bus thats too loud, or saving batteries on my Game Boy). However once playing the version with sound versus without, it's easy to see what I was missing. Sound helps drive the experience and all the aspects of sound mesh together help create the full cohesive experience of the game we are playing. Weakness in area can have surprisingly bad consequences for the experience if it's that bad or disengaging.
As Professor Kapralos said, sound is an important but often neglected part of games.