Connotative meanings refer to secondary or associate meanings as opposed to direct or literal meanings. An example is calling a person “steely” to mean that they are determined rather than that they are composed of steel.
The opposite of a connotative meaning is a denotative meaning. The denotative meaning of a word or phrase is what would be found in a dictionary under the primary definition. In the case of “steely,” the primary definition is simply that something is composed of or related directly to steel. Whether the denotative or connotative meaning of a word is meant is usually dictated by context. Since people aren’t generally made up of steel, it’s more likely that when a person is described as “steely,” the connotative meaning is meant. In this case, it serves as a metaphor to express that the person is resistant to change emotionally in the same way that steel is resistant to change physically. In some cases, both the denotative and connotative meanings might apply in a deliberate play on words. For example, someone might describe a robot made of steel as having a “steely resolve,” which means both that the robot is determined and that it is actually made out of steel.