What you're most likely looking for is amateur (ham) radio. The exactly regulations will vary by country, usually there's some sort of testing/licensing required (at least if you want to transmit, you can listen without a license)

I didn't look too far into it but it looks like the app you linked is basically a tool to let you use your phone as a controller for other radio equipment. You'd probably need to be licensed to actually use it, and there's a good chance the equipment needed is pretty pricey. Ham equipment can kind of run the gambit from handhelds that run from about $20 up to thousands of dollars depending on what you want to do with it. You're probably better off starting with some more standard equipment before you start trying to rig together other stuff controlled by an app.

There's a lot of info out there for free on the internet and plenty of books have been written about how radio, so there's a lot of resources out there to learn from, or if there's a radio club in your area (there usually is) you can show up to a meeting and ask some questions.

Assuming you're in the US (different countries again have different laws) there's a few other radio options if all you want is to talk to people who are local to you. You can get a CB radio (think Smokey & the Bandit or truckers talking to each other) some places have more or less people actually using CB radio. The range and capabilities are more limited than a lot of ham options, but you can usually count on a few miles of range, and sometimes it's nice to get a heads up from truckers about traffic issues and speed traps and such. I personally like to use them with friends in different cars when we're on a road trip.

There's also FRS radios, you can pick them up pretty cheap at Wal Mart, pretty basic walkie talkies.

Many of those FRS radios are also GMRS radios, there's a GMRS license needed to use the GMRS capabilities, not test, just a licensing fee, so that's something to be aware of.

MURS radios also exist, I honestly don't know too much about it, but it's another free, no-license radio service you can use.

Each of those have their own limitations and restrictions on what you can do with them, but in probably 99% of cases you're probably not gonna run afoul of the law if you don't try to modify the radio or do something obviously stupid and use it in a way that's not interfering with other people's uses.