While Nim did indeed accomplish a great deal signing, whether or not he actually accomplished language is another matter entirely (for more information on this type of debate, see Koko). The moniker given to Nim had a good deal to do with Noam Chomsky's theory of human linguistic development. Chomsky advocated the idea of a language acquisition device (LAD) in humans that facilitates the vocabulary explosion that children typically experience around age 2 or 3, and a universal syntax that had to do with a subsequent and dramatic increase in the complexity of sentence structures used by children. Chomsky essentially held that for use of 'human' language, an innate cognitive component was necessary. Whether or not Nim could successfully use ASL, and just how his abilities progressed, would show how valid Noam's idea was.
The benchmark for comparison used in gauging Nim's linguistic abilities in the scientific literature was the mean amount of signs 'strung together' in a series (if you're willing to take a bit of a leap, that translates to mean length of a sentence1). Figures on Nim's signing lengths were compared to the mean length of utterance, or MLU, of toddlers.
Nim's development, did, in fact, mimic that of humans up until the age of 2, namely a slow, linear increase in available words and length of utterances. At that point, the paths separated. Nim's vocabulary expansion continued in a roughly linear fashion for the next few years, while his human counterparts began acquiring words rapidly, at a rate of nearly 5 new words uttered a day. Perhaps more importantly, Nim's MLU peaked at an average slightly above 2 words per utterance, while the human children's MLUs not only continued to increase, but at a much higher rate than before.
Nim certainly was able to communicate using signs. However, his development ultimately supported Chomsky's idea of a necessary innate component for what we call language. It's possible from a behaviorist standpoint to say that Nim's development reflects more of a memorization of symbols than anything else, as he never really demonstrated proficiency in the structure of his language. However, most scientists in the field will at the very least concede that Nim was communicating clearly.
The debate on what level of linguistic knowledge Nim and other apes possess(ed) has been a heated and sometimes spiteful one. Critical members of the scientific community will often accuse the trainers and caretakers of these apes of giving their apes more credit than they deserve; trainers will state that some scientists put humans on too high of an intellectual plateau in comparison to apes. There is probably a little truth in both arguments. However, Nim certainly accomplished what scientists and linguists had hoped for, namely greater insight into the necessaries of language acquisition, and into the general forum of nature vs. nurture.
1As for the internal validity of this measure, YMMV. In studies of Koko, 'sentence' length often increased by repetition alone; examples include "Look water bird water" and "eat banana eat banana." It is also worth noting that for toddlers, similar grammar and vocabulary expansion is observed in English-speaking children and children who use ASL, so one may assume that the vocal/gestural difference between Nim and the children studied was not a profound factor in the eventual results.