Your taxes for 2015 are due on April 15, 2016. The extension allows you to do your paperwork later - but if you owe taxes, it doesn't allow you to pay late without paying interest. And if you're due a refund you don't get the refund until you actually file.
The first date of your income that is on your April 15, 2016 return is 1/1/2015, and the last date is 12/31/2015. I believe the last day for 401k contributions is 12/31/15 also. You can contribute to your Traditional or Roth IRA until the filing date/original due date of the return, however - so you can fund 2015's IRA any time from 1/1/2015 until 4/15/2016.
Got it? :P