In cognitive linguistics, a conceptual metaphor refers to the understanding of one idea or conceptual domain in terms of another. Based on this definition, the formula for a conceptual metaphor is: Target Domain (TD) is Source Domain (SD). Conceptual metaphors can be recognized in everyday language. They shape the way we communicate, think, and act. In Lakoff and Johnson’s influential work Metaphors We Live By (1980), they argue that everyday written and spoken language is often filled with conceptual metaphors, even though they may go unnoticed. Here are some common examples:

• Life is a journey
• Arguments are war
• Love is a journey
• Time is money
  (Lakoff & Johnson, 1980)

The two domains involved in a conceptual metaphor have specific names. The source domain (SD) is the conceptual domain from which we draw metaphorical expressions, while the target domain (TD) is the conceptual domain that is understood through the metaphor.

In the examples above, "life," "arguments," "love," and "time" are target domains, while "journey," "war," and "money" are source domains. The target domain is what we try to understand, and the source domain is the more concrete or physical concept used to structure that understanding. A key generalization is that conceptual metaphors usually map a more concrete source domain onto a more abstract target domain.

To generate a conceptual metaphor, knowledge from the source domain must be mapped onto the target domain. In other words, the source domain is where the concept is mapped from, and the target domain is where the concept is mapped to. This is commonly represented as:
TARGET DOMAIN IS SOURCE DOMAIN, which defines the conceptual metaphor. 

For example, when people understand love in terms of a journey, the conceptual metaphor LOVE IS A JOURNEY helps structure their understanding of the concept of love. However, this conceptual metaphor is not usually stated directly. Instead, it is realized through metaphorical linguistic expressions, such as the following:

• We’ll just have to go our separate ways.
• Look how far we’ve come.
• It’s been a long, bumpy road.
• We’re at a crossroads.
• We can’t turn back now.
• Where are we?
• Our marriage is on the rocks.
• We’re stuck.
• I don’t think this relationship is going anywhere.
  (Kövecses, Z., 2010)

From these examples, we can see that the way people talk about love in English mirrors how they talk about a journey. People use the concept of a journey to understand the abstract concept of love.

A set of systematic correspondences between the source domain and the target domain forms the basis of conceptual metaphors. These correspondences are called mappings. Let us revisit LOVE IS A JOURNEY as an example. The following mappings exist between the two domains:

As shown, the constituent elements of the conceptual domain JOURNEY systematically correspond to those of the domain LOVE. The application of the journey domain to the love domain provides the concept of love with a particular structure and set of elements.

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