PEG channels are channels set aside for Public productions, Educational programming, and Government programming. They are set aside by the cable or satellite provider in a given community, usually in partnership with that community. Some larger communities will also have smaller similar channels for churches, or a local college, in addition to the usual three. You might see them listed as "Local Access" or simply "Access" channels. They are generally paid for with a percentage of the money paid each month to the consumer's cable or satellite provider, as well as (particularly with educational or government channels) tax money. They are divided up into categories based on the type of content they provide:
Public channels are channels that produce and broadcast content by and for members of the community. Some communities have restrictions, such as that amateur producers must take a course on how to produce TV content (generally offered by the network), or that they can't be making any productions for profit (as the networks themselves are usually non-profit). As far as content goes, there are few restrictions on the type of content it can be, so long as it is not vulgar, obscene, or hateful. Not many people use this avenue of video production and sharing anymore, with the advent of video-sharing websites such as YouTube and Vimeo. However, they do offer the advantage of genuine TV equipment and studio sets, something your average YouTuber might not have access to, and they can be a good place to start if you want to get into television production. They may also show broadcasts of events in the community, or even local news.
Educational channels produce content usually intended for distance-learning. (Think Homeschooled Kids, and adults who are taking Correspondence Courses, or studying to get their GED.) They may also be used by school systems to let parents know about the goings-on at the schools, such as the first day of the schoolyear, or the holiday pageant, or a bake sale. Most often, they air the local school board meetings.
Government channels generally show things like the minutes of town or city council meetings, or such meetings as they occur. (Think C-SPAN, but on a local level.) They may also be used to alert residents of a town or city of changes to local laws or tax policies, reminders of upcoming elections and how to register as a voter, or for local campaigns (for positions such as mayor, or city council.)
Some other channel types follow a similar format, but are not, strictly speaking, PEG Channels. These include:
Leased-Access channels: These are similar to the Public channels, except that their productions can be for-profit, and the channels are funded (in whole or in part) by ads for local businesses. In the past, No Budget affiliates of UPN or The WB or religious stations which couldn't get regular cable carriage would use these channels to get their primetime programming on a cable system somehow. In practice however, leased-access channels are now the domain of 24-hour national Infomercial channels since local advertising has moved to the Internet and cable providers needed someone to pay for the channel space.
Municipal Access channels: Similar to PEG channels, but may also be used to create content for an institution such as a church, an N.G.O. in the local community, a private school, or a college. (Similar to College Radio.) These may be paid for with funds from the institution, the community, cable or satellite bills, or any combination of the above. They are, however, almost always non-profit.