What is a SPSite and SPWeb object, and what is the difference between each of the objects?

The SPSite object represents a collection of sites (site collection [a top level sites and all its subsites]). The SPWeb object represents an instance SharePoint Web, and SPWeb object contains things like the actual content. A SPSite object contains the various subsites and the information regarding them.

SPSite : Site Collection
SPWeb: Sub-site