Continuous Integration, Delivery, and Deployment are relatively new development practices that have gained a lot of popularity in the past few years. Continuous Integration is all about validating software as soon as it's checked in to source control, more or less guaranteeing that software works and continues to work after new code has been written. Continuous Delivery succeeds Continuous Integration and makes software just a click away from deployment. Continuous Deployment then succeeds Continuous Delivery and automates the entire process of deploying software to your customers (or your own servers).
If Continuous Integration, Delivery, and Deployment could be summarized with one word, it would be Automation. All three practices are about automating the process of testing and deploying, minimizing (or completely eliminating) the need for human intervention, minimizing the risk of errors, and making building and deploying software easier up to the point where every developer in the team can do it (so you can still release your software when that one developer is on vacation or crashes into a tree). Automation, automation, automation, automation... Steve Ballmer, would say, while stomping his feet on the ground and sweating like a pig.
The problem with Continuous Integration, Delivery, and Deployment is that it's not at all easy to set up and takes a lot of time, especially when you've never done it before or want to integrate an existing project. However, when done right, it will pay itself back by reducing bugs, making it easier to fix the bugs you find and producing better quality software (which should lead to more satisfied customers).