Explanation I use in comments on student papers:
Consider the following hypothetical correct sentence: “Laughing all the way, the children ran to the playground.” Here the modifier phrase (“laughing all the way”) correctly modifies its noun (“children”). By contrast, consider the following incorrect sentence: “By allowing different options for navigating, the reader takes on the role of narrator as well.” Here the modifier phrase (“By allowing different options for navigating”) seems to modify the noun “the reader,” whereas the sense of the sentence is really as follows: “By allowing different options for navigating, the author of the work allows the reader to take on the role of narrator as well.” (That is, the phrase modifies “author.”) We speak of such a modifier phrase as “dangling” because it is a loose strand isolated from its true referent. Dangling or misplaced modifiers usually occur when the modifying phrase points toward the wrong noun in a sentence or when the noun that the phrase should modify is missing.
Version 2
A dangling modifier or phrase is one that does not seem to refer to anything named in the sentence or seems to refer to the wrong thing. This is often because the phrase is syntactically out of place in the sentence (usually at the beginning). Thus consider the hypothetical sentence, “Inherent within the text, Donne argues that the only thing constant about a woman is her inconstancy.” Here, it is unclear what the dangling phrase “inherent within the text” modifies, unless it is “Donne” (which would be odd). Here is another example: “After studying the author’s argument, the essay seemed to prove its point.” (_Someone_ has finished studying the author’s argument, but he or she is not named in the sentence, with the result that the initial phrase is dangling free.)
Writing problem: this is a classic “dangling modifier,” meaning the sentence structure makes the phrase seem to be a modifier of the wrong object or subject. In this case, it seems that “many plays” are “looking at this period.”
