What does dominant generation mean
According to "Wile, Dr. Jay L. Exploring Creation With Biology. Apologia Educational Ministries, Inc. 1998" and reported here, 


  In alternation of generations, the dominant generation is the generation that occupies the largest portion of the life cycle


I guess that it has to be understood in terms of "time". I am not quite sure though if it has to be understood in terms of generation time of life span. Intuitively, I would say that generation time would make much more sense. Therefore, I'd say that, the dominant generation is the generation which have the longest mean generation time (=mean time from the birth to reproduction).

As @Shigeta said in the comments: For example, in Homo sapiens, the dominant generation is the diploid phase (sporophyte, you and me) and the non-dominant generation is the haploid phase  (gametophyte, sperm/ovule).