When importing your images into Lightroom you have four options as to how to handle their location and file type. The first option, "Copy as DNG", is actually the only option that changes the file type and is the one that I use and recommend you use as well (I explain more in this post here). It converts your image into DNG format and copies the image from your source (likely a memory card) to a new destination (likely your main hard drive). Next, the "Copy" option does pretty much what it says, simply making an exact copy from your source to your destination. The "Move" option takes the images from your source and transfers them to your destination, removing the files from the source in the process. And lastly the "Add" option simply adds the information to the Lightroom Catalog but does not change the location of the image file.
So when would you use these different options. I will start by saying that when you are importing images from a memory card, like we commonly do, the options to "Move" and "Add" are not available. Why not? Well, neither option ensures that you have a copy of your images (Adobe makes the assumption, out of caution, that you will be importing images via a memory card that is likely to be reformatted or deleted) and Adobe doesn't want to hear it if you accidentally delete your images from your memory card after using the "Move" or "Add" option - leaving you with no actual images. So an example of when you would use the "Add" option would be if you have a hard drive of images that you want imported to Lightroom (remember Lightroom really just wants to know where your images are - database system) but don't plan on relocating those images - say an older hard drive that you don't necessarily use much but might at some point . An example of when you would use the "Move" option would be if you have images on a hard drive and you want to place those images on a new hard drive - maybe when your current hard drive is getting low on space and you need a bigger drive. Both of these methods ensure that Lightroom knows where your images are but neither creates a copy of your images. The "Copy" option does exactly what it says. It takes the images, again commonly from your memory card, and copies them to your destination folder and of course gives the Lightroom Catalog the info it needs - file location, metadata etc. Lastly, "Copy as DNG" does the exact same thing as "Copy" - copying images to a new destination, informing Lightroom of file location and metadata - BUT it also converts the image to the .dng format. DNG is essentially an Adobe created RAW file format but it definitely has benefits (see this) and adds a bit of insurance.
Just to review, "Copy as DNG" - YES
"Copy" - Maybe
"Move" - NO
"Add" - NO
Let me know your thoughts and questions in the comments below!