What the different between full text and peer review
The two choices are limiters; they will limit what results are shown to you.
The "full text" limiter will only show you articles that are fully available when you click on the title. That is, you won't be shown all the articles that exist for that search, only those that exist in our system as the full article. Most of the articles listed can be "borrowed" from other libraries in 24-48 hours, so limiting to "full text" really cuts out great material that you could have in 1-2 days. I don't recommend using "full text" as a limiter unless your paper is due in less than 24 hours and you are just now starting to do the research.
"Peer review only" limits the results list to those articles that have gone through the "peer reivew" process. Typically, an author writes an article and sends it to the editor of a journal. That editor will then send copies to two or three experts on that subject (they are called peers). Those reviewers then determine if the article should be published, trashed, or if it needs a few changes. They then send their thoughts back to the editor. The editor then sends it to print, or sends it back to the author with recommendations to make the article better. In the end, the peer review process improves the quality of the article being published. Most instructors require that articles be "peer reviewed". They also might call them "academic", "scholary", or "refeered". Those all mean the same thing.