If you already know what "The Cloud" is then you can skip the following paragraph, otherwise please read on:
The easiest way to understand the cloud is to think of it as a utility, like electricity. When you plug a device into a wall outlet, electricity flows. You didn't generate the electricity yourself. In fact, you probably have no idea where the electricity was generated. It's just there when you want it. All you care about is that your device works. Cloud computing works on the same principle. Through an internet connection (the equivalent of an electrical outlet), you can access whatever applications, files, or data you have opted to store in the cloud--anytime, anywhere, from any device. How it gets to you and where it's stored are not your concern (well, for most people they're not).
I've collected a few cloud based applications/services here that might be of interest to the radio amateur and/or experimenter. They look like they should stick around for a while and have already reached a fair level of maturity:
circuits.io: Described as a free circuit editor in your browser, it is actually a lot more. You can not only design practically any kind of circuit using just a web browser, you can turn that circuit into a printed circuit board and then BUY that PCB board online. Several different technologies had to come together to make this into an effective tool. This tool is fairly new but is becoming very popular. Hopefully it will stick around and continue to mature into something great.
WebSDR: While arguably not a "cloud application" it does allow you listen to software defined radios, using a web browser, from anywhere you have internet access.
There are multiple sdr receivers located across the globe using a variety of receivers and antennas. Some are tuned to the HF bands while others cover VHF & UHF bands.
This is an invaluable free service provided by institutions and individuals at their own cost.
APRS.fi: The distributed network of Automatic Packet Reporting System stations, repeaters, clients and map servers could be considered to be "of the cloud" before the cloud even existed. With an APRS equipped radio you can log your position from a GPS, over the air & through another ARPS receiver. This is then sent out (usually) across the internet to other systems which in turn can map your location or update other APRS clients or radios. APRS has also been extended to include the ability to text message which is particularly useful in locations where cell phone SMS messages or email are not possible!
Echolink: Like APRS, Echolink links the Internet to amateur radio. However Echolink links the audio and PTT (push to talk) signals from a radio or software client to a radio in another physical location. If you're stuck in a hotel room or another location without access to a radio you can still "get on the air" using an Echolink client on your Windows, Linux, iOS or Android computer & handheld device. Most Echolink connected stations are VHF/UHF but there are HF stations connected as well. Echolink is not designed to replace radio to radio communications but instead increases the connectivity of amateur radio operators and allows hams, who otherwise would not be able to operate, the pleasure of getting on the air.
As you can see, some of these "cloud apps" pre-date the idea of cloud computing by quite a while. Just another example of amateur radio folks being ahead of the curve without even realizing it.