This is sparked by Franzis Black&White Projects app being on GOTD -- thought it might be useful to expand a bit on creating B&W photos.
1st off, a true B&W digital image only has black & white -- no gray, which is simulated using dithering, which refers to the pattern of how the black dots are spread out, with more spacing appearing as a lighter gray. Black & White photos are actually gray scale. You can scan a photo to a gray scale file, but you'll capture less data -- the gray scale image file itself stores less data. You probably can't take a B&W photo -- if the camera gives you that option it's likely a color photo that's been converted in-camera -- though some will allow you to preview the shot, before you take it, in B&W.
A color image file stores luminance -- the lightness values of pixels from black to white -- and color data, which you can often separate to some extent in image editing software. A standard quick conversion from color to gray scale just keeps the luminance data & tosses out the color info. Editing the color image before the conversion makes sense -- one, you've got more data to work with, & two, it can be easier that way, e.g. you can make the blue in the sky lighter/darker fairly easily, but try darkening just the sky in a gray scale version.
More advanced color to gray scale conversions map the colors in an image to shades of gray, e.g. B&W Projects & P/Shop / Lightroom. This gives you more subtle control, plus it's more interactive, but the basic principles stay the same... you can darken the blue in the sky before a simple gray scale conversion, or you can interactively lighten or darken the blues in P/Shop / Lightroom, or you can adjust the same settings in B&W Projects.
Anything that changes the colors, their saturation, &/or lightness/darkness [luminance] values effects what you see in the resulting B&W photo. In P/Shop / Lightroom you can adjust the levels, curves, & White Balance, in addition to changing the intensity & lightness/darkness of a dozen or so colors, which all interactively changes what the B&W version looks like. You can also change hues, adjust the overall [all the colors] lightness & darkness separately, adjust clarity & dehaze etc., which again let you fine tune the color -> B&W conversion. And if/when working in P/Shop / Lightroom, you can also use bracketed shots for or with HDR, making up for the exposure limitations of cameras -- there are just some shots where the exposure setting that gives you detail in the sky turns the landscape into mud for example.
And that's the good & bad of an app like B&W Projects... You can't make all of those [potential] adjustments, because B&W Projects isn't a complete image editor, which is bad from the standpoint that you lose lots of flexibility [maybe think of it as possibilities], but that's also a load of possible settings or adjustments that you don't have to worry about, which is good if all those settings make you feel overwhelmed. While there are a 1/2 dozen or so sort of templates for B&W in P/Shop / Lightroom, 99.9% of a color -> B&W conversion is going to be trial & error, where in B&W Projects you start with a bunch of presets with thumbnail previews.
IMHO, in actual use B&W Projects has one big limitation -- if you want quick & easy, the photos you feed it have to be clean. I've been scanning all of our old photos, so I tried what was a technically-speaking somewhat poor snapshot in the Franzis app [it was just the 1st photo in the folder], and in the presets it did horribly, though v.5 is a big improvement on v.4 in this regard. There's a bit of noise if you zoom in on the image, which B&W Projects overemphasized, while the image itself was overly dark with little in the way of mid-range grays. Using the same photo, a simple color -> gray scale conversion in PaintShop Pro, & the initial image using Photoshop's Camera Raw in B&W mode [before any tweaking], both looked tremendously better. I'm sure you could get there in B&W Projects after playing with the settings, but the point of the presets is you shouldn't have to.
The reason I bring that up is that we've got a roughly $200 Kodak Point & Shoot, and the pictures it takes actually have more noise than than the scanned image I tried in B&W Projects. And that Kodak's not alone -- digital cameras that take very low noise photos are the exception rather than the rule.