RSpec is a 'Domain Specific Language' testing tool written in Ruby to test Ruby code. It is a behavior-driven development framework which is extensively used in production applications.
Cucumber can be used for System and Integration Tests.
The main difference between RSpec and Cucumber are the business readability factor. Cucumber's main draw is that the specification (features) are separate from the test code, so your product owners can provide or review the specification without having to dig through code. These are the .feature files that you make in Cucumber. RSpec has a similar mechanism, but instead you describe a step with a Describe, Context or It block that contains the business specification, and then immediately have the code that executes that statement. This approach is a little easier for developers to work with but a little harder for non-technical folks.