I just want to add a comment: because the sounds are drawn randomly, everyone hears something different! So, comments like "it does sounds more like a brook" may be right, but just for one particular user, and particular occurence.
Today, the average visit duration time is about 30s... and it takes my engine about that same time to evolve from one sound to another. If you think that you are not hearing something that does sound like rain to you, either reload the page (it will start all over again with a new draw) or give the generator a longer listen, like two minutes (I know, this is a lot of time, on the Internet). Then, you will understand why this rain noise generator is different from others. It really shines over longer listening sessions.
How it works? Basically, I have sounds in four categories: Light Rain, Heavy Rain, Thunder, and Water sounds (like those occurring once the rain has stopped). The generator starts by choosing one of these categories (with higher probabilities for the rain, but sometimes, it can start with the water sounds - hence that user comment). For each category, there are dozens of different recordings. So, even if you keep playing rain from the same category, it will keep changing. Staying in the same category or switching to another is governed by a very simple transition probabilities matrix.
Also, you can change the spectrum of the rain (white/pink/brown) by means of the pencil (this setting affects the next draws, so its effect is not instantaneous). Being able to change the color of a natural noise, is an interesting feature, IMHO.
As a qualified "rain sound critic", to my ears the generated rainfall didn't sound convincingly natural. Real rain is somewhat less "white" (lets call it "gray"), with a steadier, if muffled "thud" as drops hit land.
Of course there are many variables, like wind speed, rate of rain accumulation, soil conditions, urban vs. rural location among others, that alter rain's sound qualities. Accounting for these factors would probably be quite difficult. Too bad the website didn't provide more info about the sound generation algorithms, I think HN readers would appreciate that.
As far as applications of generated sounds go, I think it's a very individual matter. In respect to tinnitus, a condition I've had for a long time, it's not a problem only when things are quiet.
In my case the internally generated high-pitched squeal is constant, loud enough to interfere with normal conversation. Adding external noise doesn't decrease or "mask" the tinnitus, just makes it harder to distinguish sounds in the environment.
One more thing, having known hundreds of adults with ADHD, mileage varies considerably re: benefit or decrement of background sounds on concentration. Offhand I don't know of studies documenting effects, but it would be an interesting study to conduct. My guess is most would do better in a quiet, but not too quiet environment. The issue is precisely what is "quiet" or "too quiet" for these individuals.
I also have tinnitus, but it's nowhere near as bad as yours sounds. Something like this is more than sufficient for me to mask it. It's really only an issue for me when things are very quiet.
Anecdotally, I find it much easier to concentrate with extremely loud music, usually with a strong and at least moderately fast beat. Even if I were to turn this up to 11, I don't think it would help me very much, aside from possibly masking background sounds that might grab my attention. At normal levels, I don't see it making any difference at all.
A slider to adjust the level of white noise (and maybe some other spectral properties) could be just the ticket.
But please understand this is a white noise machine too. The rain sounds that have been selected - especially the heavier rain sounds - do include a high level of white noise, naturally.
The basic concept is surprisingly simple: each generator is actually a collection of 10 looping sounds, each ostensibly covering a given frequency range. You can achieve really different resulting sounds my adjusting each channel. See for example the different presets (on the middle right of the page) for the Crystal Stream generator. 
I'm impressed by the quality of work that Stephane Pigeon put into each of these, and I'm glad he's marketing it well with rain.today :)
Edit: I see discardorama asked the same question.
play -c2 -n synth whitenoise band -n 100 24 band -n 300 100 gain +20
It became so bad that I could barely get an hour or two of continuous sleep a night.
Finally, I found a bunch of videos: https://www.google.com/search?q=rain+white+noise&tbm=vid and started playing them at night. Boy, what a difference it made. Now, I wake up at most once a night; I'm sleeping better than ever, and not a zombie during the day.
I'm wondering if there are any command-line rain generators for Linux? And is there some research on how to generate the 'best' (most realistic?) rain sounds.
I think if you don't do this early getting them to accept it later will result in them singing you the song of their people at 3am.
Possibly the cat.
Clearly you have never had a cat, if you're asking that question.... ;-)
These are two I've tried out:
http://sccode.org/1-e -- Rain and thunder (for supercollider)
http://www.obiwannabe.co.uk/tutorials/html/tutorial_rain.htm... -- for PureData
The rain does sound somewhat whitenoise-y though, I wonder if there are any simulations of rain, that take into account the actual physics of droplets hitting a surface.