Why are people interested in studying the interstellar medium? It turns out that the interstellar medium is pretty exciting stuff! The primordial interstellar medium was formed in the Big Bang, which is currently thought to have occurred some 15-20 billion years ago. The matter in the Universe produced in the Big Bang was not very diverse, being made up of mostly hydrogen and some helium, with trace amounts of lithium, beryllium and boron.
The first stars were born quickly after the formation of the first galaxies, and lived exciting but quick lives; inside of these massive bodies, new elements were formed by fusing the the lighter ones together. The end of these stars` lives were seen as gigantic explosions -- supernovae -- where even more elements were formed before they were spewed out into the interstellar medium. The new elements which were created now fill up the Periodic Table -- carbon, nitrogen, oxygen, silicon, iron, cobalt... all the way up to uranium and beyond.
The interstellar medium now contained many new elements, because as old stars die, their matter is swept back into medium from which they were created. Since the interstellar medium is also the birthplace of new stars, the next generation of stars (and some solar systems) contained these new elements -- the elements on which life as we know it depends. Everything in the universe is recycled. In essence, we are the children of supernovas and the Big Bang: every atom in our bodies was formed somewhere out in space, and has been recycled many times before it joined our bodies.
Here are more reasons we are interested in the interstellar medium: