Yes, partial transit will consist of your provider's peering routes (often their own plus routes bought in from another tier 2). Since your upstream provider isn't paying transit rates they will often offer you the partial transit at very low cost.
You will need a BGP router and at least 1 full transit provider to take advantage of this unless you only want to be visible to half of the internet! As BGP will by default prefer the shortest path (in terms of AS hops), your partial feed will often be used over your more expensive full transit thus saving you a little money and (in theory) improving your network + latency to your users.
If you're asking these questions, you probably won't find this worth the hassle - there are plenty of companies out there who will sell you IP transit for peanuts if your usage is large enough to justify the above setup. Alternatively you could look for a consultant to help you set up your AS.
HTH, good luck
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