A continuation patent application can be thought of as a “child” application of an earlier filed “parent” application, in a way similar to a divisional application. The continuation application must be filed while the parent application is pending.
A continuation application is often filed to introduce into the application a new set of claims and to establish a right to further examination. Continuation application does what it’s name says, it “continues” the examination and prosecution of the application. It is one way to keep negotiating with the patent office (another way is to file a request for continued examination (RCE)).
Unlike a divisional, the new or amended claims in a continuation application are not necessarily directed an independent or distinct invention.
The Manual of Patent Examining Procedure provides that a continuation application “is an application [e.g. a child application] for the invention(s) disclosed in a prior-filed copending  nonprovisional application,  international application designating the United States, or  international design application designating the United States [e.g. parent application].” MPEP 201.07. It also provides, “The disclosure presented in the continuation must not include any subject matter which would constitute new matter if submitted as an amendment to the parent application.”
Therefore, no new subject matter can be added in a continuation application. Rather, the continuation application merely claims an invention that was already described in the original parent application.