Oracle Access Manager, or OAM for short, is a system that allows you to allow or deny users access to resources. In other words, OAM is the authorization part of AAA (authentication, authorization, accounting).
Webgate establishes communication between HTTP web servers and OAM. Webgate is a collection of files (aka binaries) that are installed on a server.
As an example, let's say only certain users should be permitted to access www.example.com. When navigating to www.example.com, users can be presented with a basic authentication form. After the user provides a valid username and password (authentication), the user can either be allowed or denied access to www.example.com (authorization). In this example, the user was denied access (not authorized).