Olefin Carpet is also known as polypropylene and is a synthetic fiber.
Reasons to choose Olefin:
Olefin is solution dyed, meaning the color goes all the way though the fiber, (think carrot instead of radish) this means it's incredibly hard to stain, and it's color will not fade in sunlight.
The price is good. It's some of the cheapest carpet on the market.
It's mold and mildew resistant because it is extremely hydrophobic. Water will pass right though Olefin and individual fibers will float. Because liquids can't absorb into this fiber drys fast, and mold doesn't grow.
Here are a few pictures of Olefin carpet in my own home at different magnifications levels.
Reasons NOT to choose Olefin:
Although repels water, it absorbs oil. any oil based spills will be incredibly difficult to remove.
Olefin carpet has a very low relative melting point. The friction from dragging furniture across the room can provide enough heat to melt the carpet.
Olefin Carpet is not very resilient, Other carpet fibers will spring back to life even after repeated crushing, but Olefin carpet doesn't hold up to traffic very well. Once it gets matted down you are going to have a traffic pattern that will be noticeably different then the carpet in lighter traffic areas.
To overcome the poor resilience of this fiber it is often sold as a short looped or berber carpet. The short tight pile makes it so if it is worn, crushed and matted, at least it's less noticeable then if it was a plush cut pile.