The term "magnum" in firearms usage came about in 1912 from the firm of Holland & Holland, when they introduced their .375 H&H Magnum rifle cartridge.
Taking the word from the French champaigne industry, where magnum meant a larger than standard size bottle, they applied it to the name of their new round. Over the years, it has retained its general connotation of "larger than standard case" inferring more power, and higher velocity because the "magnum" holds more powder (and is commonly loaded to higher pressures) than the "standard" case.
Magnum is a marketing term, with no specifically defined meaning, only a general one. And, how much more than "standard" a magnum is depends on what one uses for the standard.
Some magnum rounds are direct developements of previous cartridges, others are not.
There is no linear, or even consistant relationship between the energy & velocity (power) of cartridges based on caliber (bullet diameter). One has to look at each one individually, and consider the size of the case (amount of powder) and the pressure it is loaded to, along with the size & weight of the bullet.
There are many examples of some cartridges with smaller bullets, having greater energy than some with bigger bullets, it depends on the speed the bullet is fired at. For example, a .357 Magnum has more energy than a .45ACP, because the .357, while firing a smaller, lighter bullet than the .45 is firing it much faster.
And, as to "why is there air?" The simple answer is "so we don't exhale ourselves to death!"
