The wording you quote in your question is actually only part of the author's sentence. Here is the entire paragraph in which the complete sentence occurs, from Frank Close, Antimatter (2009):
All cultures have wondered about their origins, and the paradox of how something came from nothing. Why the Big Bang occurred no one yet knows, but out of its energy everything that we know was born. And it is beams of antimatter, first antiprotons and then positrons, that have enabled us to simulate the early universe in experiments, and begin to understand what it was like when less than a billionth of a second old. This is an astounding achievement of the human intellect: of groups of atoms collected together and able to think, to look out in wonder at the universe that made us, and build machines that can revisit our origins in the Big Bang. And the tool that made this possible is antimatter. With such inspirations in fact, who needs fiction.
The entire block of text that you quote ("of groups of atoms collected together and able to think, to look out in wonder at the universe that made us, and build machines that can revisit our origins in the Big Bang") amounts to a much-elaborated alternative way of expressing the last four words of the preceding portion of the sentence ("of the human intellect"). Replace the latter with the former, and you get this coherent wording:
This is an astounding achievement of groups of atoms collected together and able to think, to look out in wonder at the universe that made us, and build machines that can revisit our origins in the Big Bang.
It is somewhat more common nowadays for authors to signal this type of amplifying construction with an em dash (—) than with a colon (:), but the author is well within his rights to use a colon here. Another option would have been to use a comma in place of the colon, but that punctuation would have been a bit weak to clearly establish the equality that the author wanted to assert between the two blocks of text that I identified in parentheses above.
With regard to your question about whether "was" is needed before "able to think," the author would not have used "was" in any case, but he might have expressed himself more completely by including the bracketed words below in his sentence:
This is an astounding achievement of the human intellect: of groups of atoms [that have] collected together and [are] able to think, to look out in wonder at the universe that made us, and [to] build machines that can revisit our origins in the Big Bang.
Such omissions are so common in speech and writing that listeners and readers become adept at filling in the blanks, so to speak. But for a language learner, the task can be quite challenging.