Who doesn’t like benzene rings? They remind me of little molecular donuts. Too bad these donuts would probably give you cancer.
Benzene was first discovered Faraday in 1825, but did not know its structure. In fact it took 40 years before Friedrich Kekule discovered the structure that we so lovingly know today. Benzene is unique because it has a delocalized (meaning the electrons are spread out over several atoms) electron system. Instead of being localized on each carbon atom, the electrons are spread out in a ring like system as seen below (source):

Compounds that have a delocalized pi system like benzene are typically called aromatic molecules. Aromatic doesn’t refer to their odor (though they typically smell like something that has been dead for a few weeks), but just refer to the fact they contain delocalized pi orbitals. Without going into molecular orbital theory (basically MO theory describes how electrons in molecules occupy certain bonding and anti bonding orbitals), the delocalized “pi” (“pi” refers to a type of MO theory orbital) orbital makes benzene incredibly stable. In fact it takes some strong reagents to make benzene do anything at all as in concentrated nitric + sulfuric acid strong.
Like most organic compounds, benzene likes to cause cancer because you know, why not? When benzene gets into a cell, it attacks and breaks apart DNA which you could probably conclude is a very bad thing. Ironically, benzene rings are found in a ton of biological molecules and drugs as the aromatic rings allow the molecule to interact with the hydrophobic portions of the enzyme better. This is a classic example of a toxic substance being turned into something useful (and even healthy). Think about this way: Sodium by itself is explosive while chlorine is toxic and cause some terrible burns, but together they form salt which makes food tasty and delicious. Just don’t put benzene on your food though, your cells wouldn’t like it that much.