A peering is an agreement of two providers to exchange traffic for free. Since this makes only sense when they are actually able to exchange traffic between each other without any costs, a physical connection is required. This is often done via a Commercial_internet_exchange (which, contrary to its name, is not necessarily commercial), where a bunch of ISPs is connected.
Peering partners set up contracts with each other about what kind of service they provide. In some cases, peering partners also want to have money for peering or they want you to have a minimum size before they hassle to announce their routes to you.
Transit is the term for traffic you do via another ISP, i.e. this ISP is not the final goal, but just providing the uplink to other parts of the Internet. Usually, you have transit contracts with medium-sized ISPs where you pay some money (one example: 200MBit/s for 500 Euro) to have an uplink to the Internet, without having to care for peerings yourself.
These are probably only relevant in the case of community network (i.e. which may not be connected to the global internet)
TODO: contact the people who wrote these agreements.