As stated earlier, chat badges are important for Twitch chat users in the sense that it shows the status of a chatter at any time and can give somewhat of a background to help counteract the anonymity. For example, the opinion of a chatter with a long term subscriber may weigh more, to the streamer, than that of a chatter with no badges, appearing relatively new to the chat.
This badge is given to those who work for Twitch.TV itself. You don't see these often, but every once in a while Twitch Staff watch streams as well for enjoyment or for research on bans and other issues.
This badge is handed out by the streamer, usually given to close friends or very supportive chatters. It is a badge that essentially makes you immune to the chat and channel moderation settings. (Still not immune to the chat moderators though.)
This badge only appears when the broadcaster of the stream chats. In other words, when the owner of the channel speaks in chat this is the badge they will always have in their own stream.
This badge is similar to the Twitch staff badge but different in the sense that their main purpose is to review grief reports and enforce terms of service (TOS).
This badge is given to those responsible for moderating Twitch chats. These people are chosen by the streamer to enforce channel rules through time-outs, bans, reminders and more.
This badge is given to streamers who are verified partners of the Twitch website. The new affiliate program has these streamers meet certain requirements for their stream, and once verified can begin to make income.
There are a few different types of chat badges, but the main difference is that subscriber badges are typically obtained only through paying money. As shown earlier on the Bits & Badges page, when subscribing to a streamer you will get the specific chat badge they have created for their subscribers. Depending on how many subscribers a streamer has, whether they are partnered or not, and a few other factors, will affect the amount of subscriber emotes slots they have available . These slots can be used in conjunction with the extension FrankerFaceZ, which has a large, mainly user submitted, emote library that most streamers use to choose new emotes, sometimes made by their own subsribers and channel supporters.
The additional chat badges include things like:
Subscribing with Twitch Prime
Cheers and Gifted Subs (Below)
Turbo (Explained on Emotes Page)
Other (Includes things like badges for donating to Twitch Charity Events, Passes and subscriptions from e-sports channels and more.)