nLab
1-groupoid

Fix a meaning of -groupoid, however weak or strict you wish. Then a 1-groupoid is an -groupoid such that all parallel pairs of j-morphisms are equivalent for j2. Thus, up to equivalence, there is no point in mentioning anything beyond 1-morphisms, except whether two given parallel 1-morphisms are equivalent. If you rephrase equivalence of 1-morphisms as equality, which gives the same result up to equivalence, then all that is left in this definition is a groupoid. Thus one may also say that a 1-groupoid is simply a groupoid.

The point of all this is simply to fill in the general concept of n-groupoid; nobody thinks of 1-groupoids as a concept in their own right except simply as groupoids. Compare 1-category and 1-poset, which are defined on the same basis.