What should I focus on when converting photos to black and white?

• Composition - You need lines that lead the viewer's eyes through the image.
• Light and shadows - You don't have color, you only have various tonal values to distinguish one part of the image from another part.
• Contrast between different objects in the scene - This is kind of the same as the previous point, but it bears repeating. You can increase or decrease the contrast (difference in tonal values) between two differently colored objects using colored filters, either actual filters in front of the lens or digital filters when working with raw data from a bayer masked (color) sensor in the raw conversion and editing process.

Your question seems to be hinting around trying to ask, "What am I missing in the works of the great B&W masters?"

Here's what you seem to be totally missing about how the masters take B&W photos: They use color filters to change the tonal values (how bright or dark a shade of gray is) of different colors that would otherwise be the same shade of gray when converted to monochrome.

For more, please see the links embedded in the previous paragraph as well as this answer to Are there reasons to use colour filters with digital cameras?

There are a few specialized digital cameras that record only monochrome light. But if the camera used is color sensitive many of these filters can be simulated using post processing tools such as Lightroom. The limitations of a digital camera's dynamic range means better results can usually be obtained by shooting with a filter in front of the lens and sensor before the light is recorded by the sensor. Changing the color temperature in post will also affect the tonal relationship of different colored things in the scene.

Beyond that, good composition is even more important as you don't have different colors to help draw the eye from one place to the other in your photo, you only have various tones of gray.