Twenty-four hour time, or more commonly referred to as military time, is a much more efficient way of communicating. There are twenty-four hours in a day, it just makes sense.
Restaurants, businesses, airports, and pretty much everywhere besides America uses it. This is because no two times will ever be the same and then you have to specify it with a.m. or p.m. Imagine if you had a flight that left at 7:00, in this case a.m. or p.m. is extremely important. Instead, saying 07:00 or 19:00 would just simplify the matter.
Also, other countries don't call it military time, only America does because the twenty-four hour clock system is foreign to us, so we relate it to the military.
Once you are able to switch your mind from counting to twelve twice in a day (that's actually more confusing), then you'll see that twenty-four hour time is more efficient. You just subtract twelve from the number and voilá!
Stop thinking of it as always subtracting because math isn't the most fun to do all the time. Set your phone in twenty-four hour time and eventually you'll become accustomed to it. You'll love it and never want to go back.
Also, on the topic of math, if it's 7:00 a.m. and you have a meeting in nine hours, it's easier to add nine and seven instead of counting to twelve and then starting over.
It's useful for many situations. Many jobs (high end or a movie theatre) use the twenty-four hour clock. I've seen co-workers show up at 4:00 p.m. instead of 2:00 p.m. because they didn't know what 14:00 meant. That's just embarrassing.
If you're learning a language, why on earth would you ever want to say, "Oh the time is 4:00 minus 16 minutes and it's evening." My teachers always just told us to learn the twenty-four hour clock because it's easier and in Europe they'll know you're American if you don't use it.
I don't know if it's just me, but I love the confused looks on people's faces when they ask for the time and I show them my phone. They ask me what's wrong with my phone... Nothing. Just twenty-four hour time.