To help clarify- and to make sure I understand this correctly myself (please correct if I'm wrong here) - the above response from MDM applies to a conversion from a non-roth Ira into a Roth IRA. This is not really what is typically considered a back door Roth IRA.
There are 3 designations of IRAs: Roth IRA, traditional IRA, and finally a non-deductible IRA. A Roth ira and a non-deductible Ira are both funded with after tax dollars. Traditional Ira is funded with pre-tax (or tax deductible) money.
If you have all three of these IRAs and you decide that you want to convert money from your non-deductible Ira into a Roth ira, you CAN do this however you will be required to also convert a portion of your traditional IRA, which may not be advantageous from a tax perspective.
Now, a back door Roth contribution is different. Typically it is funded by rolling over after tax money in a 401k plan directly into a Roth ira. Mad Fientist has very good explanation of this. However in summary, you make a special after tax contibution to your 401k plan up to $53k/yr. then you take an in service rollover from your 401k plan and roll it direct into your existing Roth ira. Potentially allowing you to fund up to $53k/yr in Roth.
Hope that is clear and correct. If I turn out to be wrong on this, I'll just delete the post, but I think this is accurate.