It's because you're using the introduction "One of the... " which means it's referring to a specific thing. It would be the same if you said, "One of the most difficult areas of English grammar is the present perfect tense." If your sentence had been, "Some of the most common fossilized organisms are trilobites" you wouldn't need the article "the," because you'd be speaking more generally.

"One of the most common fossilized organisms" is singular, so trilobites would be wrong. It's "the trilobite" as it is referring to a specific member of "the most common fossilized organisms".

It is wrong to say "is trilobites" because with a plural you must use 'are'... You can correctly say "are trilobites" in a sentence - Except that your sentence here starts with "One of..." meaning they will later refer to something in the singular not plural. So it needs to stay "the trilobite" in this case.