Denotation is the literal meaning of a word as defined by its context. Connotation is the suggestion or implication represented by a word which alludes to its social context.
The most common example to use is the red rose. Red is the denotation of a colour, and rose is the denotation of a flower. Together they present a description of a flower of a particular colour: a red rose. The connotation of red rose is a symbol for love. The words red and rose simply describe a noun in terms of its colour and define a type of flower. Social convention has meant that the red rose as an idea represents or symbolises love.
Denotation is the dictionary meaning of a word. Connotation is the emotional overtones or nuances that the word is understood to have, but which don't necessarily show up in the dictionary.
So, for example, the words "youngster" and "child" both have the same denotation. However, they have slightly different connotations. "Youngster" seems more of a playful, light-hearted word while "child" is more neutral.
Another example is the difference in connotation between the words "house" and "home." They can both mean the same thing, but "home" has a much warmer connotation than house.
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.
Denotation refers to the literal meaning of a word, the "dictionary definition."¨ For example, if you look up the word snake in a dictionary, you will discover that one of its denotative meanings is "any of numerous scaly, legless, sometimes venomous reptiles having a long, tapering, cylindrical body and found in most tropical and temperate regions."
Connotation, on the other hand, refers to the associations that are connected to a certain word or the emotional suggestions related to that word. The connotative meanings of a word exist together with the denotative meanings. The connotations for the word snake could include evil or