The special importance of this type of (irrevocable) trust is that it makes feasible a form of gift-giving which allows the donor, (a parent, grandparent, or otherwise) to make gifts in trust, either to minors or adults, for whatever purposes the donor may have in mind, and still take advantage of the annual exclusions available for outright gifts (currently $11,000). These gifts in trust are subject to the donor's own rules (as to use, time of distribution, etc.). Without the Crummey Trust, the same gifts would be considered "future interests" (the "donee" would not have a present right to full "enjoyment" of the gift) and the annual exclusion would not be available. This tool provides very important flexibility when transferring wealth without incurring federal gift tax or using your lifetime unified credit for federal estate and gift tax purposes.
By contrast, a gift under the Uniform Gifts To Minors statutes does not allow you to impose any rules (the law-makers do that) and outright distribution must occur by age 21, at the latest. The statute provides very little flexibility of any kind, of course.
The key to being a "Crummey Trust" is the granting to the beneficiary-donee (or his/her guardian, etc.) the temporary, but absolute, power to demand immediate distribution to himself/herself. But the exercise of that power is usually most unlikely in the situations in which this technique is used and therefore the purposes the donor had in mind for establishing the trust will most likely be fulfilled.