Print size depends upon two things: Pixel count (Height & width) and Paper size (in inches or mm)
If you divide the long edge (paper or image) by the short edge, you get the aspect ratio of an image that describes the proportional relationship between its width and its height. It is commonly expressed as two numbers separated by a colon, as in 16:9 So an 8X10 sheet of photo paper can be described (when reduced by it lowest common denominator) as 4:5. Your HDTV sized monitor (1092X1080) resolves to 16:9.
Your Canon 5D MkIII has a sensor the size of a 35mm film frame (36mmX24mm and 5760px X 3840 px) It's aspect ratio is 3:2. This aspect ratio (3:2) is common for almost all cameras though some are not quite 3:2.
Now, consider printing on standard paper sizes. An aspect ratio of 3:2 can fit inside of 5:4 but there will be borders on two sides. Conveniently, LR provides a set of crop presets that match standard paper aspect ratios. They are named for the paper sizes that they match. (You can also create your own custom crop aspect ratios. If you choose the one for 8X10, you can trim away parts of the original image that will fall outside of a 5:4 aspect ratio. You can resize the crop window and move it around to select the best composition.
Once you have determined the best crop for your chosen paper, you are ready to print. This is where the pixels on the long and short edges of your cropped image become important. Lets suggest that you have made a 5:4 crop of your original image and the result is an image that is 4800X3840px (you've trimmed 960 px off of the long edge). For that cropped 4800 pixel long edge to fit onto the 10" side of a piece of photo paper, your printer will print 480 pixels per inch (ppi) if you want one with out borders. This is a good quality print. The printer will do the necessary transformation to convert pixels into dots and translate the ppi into the dpi that can be fixed by your printer.
OK, same image but a different 5:4 crop. This time the crop dimension comes out to be 800X640px and looks pretty good on your computer monitor when viewed full size. However when printing on that piece of paper, the 800px long edge is only 80ppi and the result is a pixelated image. Your computer monitor has a fixed dot pitch of ~120ppi So the full-size image on the screen is ~6.6"X5.3". A good rule of thumb for ppi for printed image is to not let your ppi drop below ~180ppi. While this is not a hard, fast rule, it does make for a good guide before printing. With the original example you could conceivable print up to 40"X32" before being pixels in the paper print.
For that 11X14 print, the aspect ratio is 11:14 and not one of the standard presets provided by LR but can easily be created using the custom option. The same rules apply and the maximum long edge of the crop is going to be 4888 resulting in a ~350ppi image when printed.
