Status is a big deal in the airline world, it gets your so many perks that you never knew you would fall in love with until you get the taste of life without them. Most importantly though is that elite status can make a huge difference on the miles you earn each year.
On my way to Seoul I was able to hit Platinum Status, this represent the middle tier of elite status on American Airlines. The perks for Platinum are minor upgrades with a few exceptions. Platinum is also known as Sapphire status for the Oneworld Airline partnership. Sapphire status give you access to business class lounges across the board with Oneworld airline lounges... this is slightly different for flying domestically with American Airlines. Lounges are a little place where you can get away from the regular crowds while you wait for your flight. Often there are some free snacks, drinks and the ability to order food. Lounges can be a nice place to relax away from the regular airport experience.
The big difference to me in moving up to the next tier of status is that I can now get a 100% bonus on miles earned. So for platinum status renewal it will take 50,000 flown miles, with a 100% bonus, you're looking at 100,000 miles in the bank. That is a round trip ticket to Europe in business class, or a first class ticket to the Middle East. Combine this with other ways of earning miles and your account builds up fast. I will likely carry a good 90,000 points over this year (even after spending 57000 on my first class ticket back from Buenos Aires). So I'm looking at going into 2017 with over 200,000 miles to spend. That's enough to get me some amazing flights to Abu Dhabi on Eithiad... which I what I'd really like to do. Etihad has an amazing first class product I can't wait to try out.
Elite status is really the way to go, if you can swing it, the 50,000 miles for Platinum status are really well worth it. I'd love to go for Executive Platinum (100,000 mile flown) sometime in the near future, but that is a significant amount of miles, that will probably have to wait a while.