When two autonomous systems (AS) peer, they can provide access to all their other peers or to none of their peers. This is often established as part of the each autonomous system's routing policy.
TRANSIT
Transit is when traffic that originates outside your autonomous system, and is destined for a network outside your AS is permitted to route through your AS. 'Transit peering' is the term used to describe an arrangement where an eBGP peer is permitted to communicate with your other eBGP peers. The most common use of this is when an ISP allows their customers using BGP to access all their other customers using BGP.
For example, let's say AS 1 wishes to be able to reach AS 5 through AS 4. AS 4 would accept AS 1's announcements and then pass the single best route for each destination on to AS 5. Traffic on AS5, destined for AS 1 may now transit through AS 4. Likewise, AS1 and AS 4 would need to perform as transit if AS2 wishes to reach AS 5.
2 5
\ /
1 --- 4
/ \
3 6
NON-TRANSIT
This is when you are providing one eBGP peer access to your network, but not to any other eBGP peers you might have. This is useful for when a customer is connected to two ISP's networks, and wishes to have each ISP's customers use their own connections to reach him. The two ISP's use a non-transit policy, while providing a transit policy for all their customers. All customers can reach each other, but the ISPs cannot use the other ISP to reach another ISP.