Most drives that you buy in a store will come pre-formatted for use in Windows computers. This format is called FAT32. Fortunately, it will also work on a Mac for most purposes. However, iMovie requires that the drive be formatted as Mac OS Extended (journaled). If your drive is not formatted this way, iMovie will not see the drive. The reason that iMovie behaves this way is that FAT32 drives have a file size limitation of 4GB. With video files, it is easy to have files that are larger than that, so iMovie does not let you use FAT32 drives at all.
To reformat your FAT32 drive, you will need to use Disk Utility, which comes with every Mac.
See this Video Tutorial for the details.
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