First, under IRC Section 408A(d)(2)(A), the distribution must be made either: on/after the date the IRA owner turns 59 1/2; after death of the IRA owner (i.e., to the estate or a beneficiary); after becoming totally disabled (under the Social Security definition of "total disability"); or for qualified first-time homebuyer expenses (up to a $10,000 limit and subject to other limitations).
The second requirement, in addition to meeting one of the preceding tests, is that the distribution must meet the Roth contribution 5-year rule (also known as the "nonexclusion period" under IRC Section 408A(d)(2)(B)).
The 5-year rule essentially states that five tax years must pass from when the first contribution is made to (any) Roth IRA, until a qualified distribution can be made.
Because the measurement is based on tax years, this means that a contribution to a Roth IRA as late as April 15 of 2014 will still count as a contribution for the 2013 tax year (in essence, it counts as though the contribution was made January 1st of 2013), which means the first year of a potential qualified distribution would be 2018 (because the five years that passed would have been 2013, 2014, 2015, 2016, and 2017). Notably, this means that a "5-year" qualified distribution could actually be made after less than 3 years and 8 months, as a contribution on April 14 of 2014 (made in2014 but for 2013) would allow for tax-free distributions as early as January 1st of 2018.
Notably, under Treasury Regulation 1.408A-6, Q&A-2, for the purposes of this 5-year rule the clock starts the first time any money is funded into any Roth IRA, whether by contribution or conversion. There is not a new 5-year clock for each Roth contribution, nor for each Roth account that is held. All Roth IRAs (but not Roth 401(k)s) are aggregated together to determine whether the 5-year rule is met for any/all of them (which indirectly means that rollovers from one Roth IRA to another do not change or reset the 5-year requirement). In the case of rollovers from a Roth 401(k), any years in the Roth 401(k) are not added to the years for the Roth IRA; thus, if an individual did not otherwise have a Roth IRA already, the rollover from a Roth 401(k) begins a new 5-year period, even if the Roth 401(k) itself had already satisfied the 5-year requirement (per Treasury Regulation 1.408A-10, Q&A-4(a)).
The fact that the 5-year requirements are aggregated across IRAs effectively means that once the 5-year rule has been satisfied once for a taxpayer (i.e., if you've already had a Roth for at least 5 tax years), it's been satisfied for good; in turn, this means that recent contributions may actually be eligible for withdrawal as a qualified distribution even if they've been in the account for less than 5 years, as long as the taxpayer overall has met the 5-year requirement with respect to any Roth IRA.
Bear in mind, though, that regardless of whether the 5-year rule is met, for the distribution to be qualified, it must still also satisfy the first part of the test (a distribution made after 59 1/2, death, disability, or under the first-time homebuyer rules).