What does "melanistic phase" mean in regards to black jaguars?
In this context, "phase" means the same thing as "color phase". Here's the definition from Merriam-Webster:


  1: a seasonally variant pelage color
  2: (a) a genetic variant manifested by the occurrence of a skin or pelage color unlike the wild type of the animal group in which it appears (b) an individual marked by such a variant


So it sounds as if "phase" originated in the case of animals that spent a season with a particular pelage (meaning "fur, hair or wool"), such as the snowshoe hare, which is brown in summer and turns white in winter, and the term then began to be used for animals that might be a different color from other individuals of that species. If the alternate color was caused by a recessive allele, most offspring of that individual would have the wildtype color unless bred with another double-recessive individual, and alternate offspring might spontaneously be born to wildtype heterozygous individuals, so pre-Mendel biologists might have seen it as a "phase" between wildtype generations.

As you can see from the illustrations on the snowshoe hare Wikipedia article, "morph" is much more commonly used today for this kind of visible variation within a species. Wikipedia has a fuller description of the nomenclature of this and related terms.