Since the above answer are good, I will add a new angle with examples. More importantly, I will offer some insight, hopefully, of how to use these concepts in interpreting passages.
A common misunderstanding in interpreting a passage is to look for meaning in individual words. On the surface this point sounds counterintuitive. After all, do not words convey meaning? However, some reflection will show that meaning is found in contexts, because the denotation or definition of words is broad. A brief look at any dictionary will make this point clear. Moisés Silva writes that most people would say that the word “bar” refers to an establishment that serves alcoholic beverages, but he also points out that there are other meanings as well. “Bar” can in a different context be used to refer to a straight metal object found on many windows. One could also add another meaning if one changes the context and focuses on the court of law. With a little thought, one can multiply examples endlessly. Linguists call this aspect of words, polysemy. The point is that meanings can change, even radically, based on the context. Therefore, responsible interpretation will recognize that the meaning of words is almost entirely contextual.
Connotation differs from denotation in that the former is related to the subjective and cultural experiences of individuals. For example, when a person uses the word, “father,” it will not be value free. A father may connote various other thoughts and feelings such as kindness, severity, love, or abuse. Therefore, in interpreting a passage, it will be important to ask what words connote in that particular context. Also it will be important to realize that words can connote very different notions with a change in time and place. For example, slavery has a very different connotation in Paul’s day than in North America. That Paul could boast of his slavery shows that the connotation behind the word was not entirely negative. In the ancient world, slavery could be a way up the social ladder as well as a way to gain great power. Moreover, unlike slavery in America, slavery in the Greco-Roman world was not motivated by race.