Magnification (first number, the 6 in 6x15) is how many times the image is enlarged over normal. More might seem better, but with any optical instrument, the higher the magnification, the harder the instrument is to use. This is especially true in a small, lightweight instrument like a monocular. A magnification of 5x or 6x is a very practical magnification for a monocular. It will be easy to steady and have a wide field of view to help in locate the target. An 8x will be significantly harder to steady and have a narrower field of view. A 10x will be harder to use, yet. You will see zoom monoculars, zoom monocular is never as durable as a fixed power model. 
Zeiss 5x10 T MiniQuick MonocularObjective size is the second number is the size of the front lens in millimeters. The larger the objective lens, the better the optical performance, all else being equal. Once again, though, bigger is not necessarily better. The bigger the lens, the bigger and heavier the monocular. A 10x40 monocular will be roughly about half of a full size binocular. A 5x15 will be no larger than your thumb. In terms of performance, optical quality is actually more important than objective lens size. In fact, you can have an optically excellent monocular that is also very small, if you are willing to pay the price.
