backup iMovie 10.0.7 on external HD

I have read the instructions for backing up the iMovie Library.imovielibrary on an external. I create a new library on my Passport external but it also shows upon my computer with the new event. There is no "new event" on the Passport HD. I don't know which way to turn next on this effort! How does one transfer the content from the computer so that it can be deleted to free up disc space! I am finding the instructions from Apple very vague. Hope someone can help with this seemingly easy task! I am using an iMac OS 10.10.3. Thanks in advance!