OK, lets go through them one at a time.
Patches: Not all games are made perfect. The devlopers try tomake each and every game as bug free as possible to make it thoroughly enjoyable. Even then there are chances that some bugs might creep in undetected. Here the game patches come into play.
These patches are released by the game devlopers from time to time. You need to install these patches as you would do in case of a game. After installation, these patches will take care of the bug that it was designed to take care off. Sometimes, patches add additional functionality to a game by adding a new feature. In short, patches are essential for an enjoyable gaming expirience!
Mods: Mods stand for "modifications". Most of the times, these are modifications of the original game done by the players themselves, guys like you and me who play the game. Mods can be of many types. Some can add a new feature to the game such as Max Payne KungFu mod by Kenneth Yung that gave Max Payne KungFu skills.
Then their are mods that are known as TC's or Total Conversions. Such mods change the game all together. They may change the story line, add new characters, new locations and levels. Case in point? The hugely popular Counter Strike...or even Max Payne Katana mod by MaDdieman and Straton Ace...yeah, yeah, I am a Max Payne fan allright!
Consoles: Well about consoles, the one is the one which has the X-Box , PS2 etc underit but then I guess you are asking about the other type on concole. Such a console is generally obtained by enabling the console key through specific commands. Some games allow you to access the console directly. Generally it can be accessed through the "tilde" key, the one above the "Tab" key.
The console can be used to key in cheat codes etc. The devlopers use the console to test the game while in devloping stage. I can't elaborate on this because my knowlege about it is limited, so sorry.
Walkthrus: Ah...a sight for frustated gamers. Stuck at some point in a game and desperately looking for a solution. Fear not, coz the Net has many people who have already beaten the game and ready to help you out with it. Such people create huge text documents that guide you step by step through a game, besides providing a whole lot of info on the game. Any time you are stuck, feel free to refer to a walkthru for the spicific game. You can find such types of walkthrus at gamefaqs.com
Now I hope I have covered all the bases. Have an enjoyable gaming session! Signing out!