Language and discourse are connected at a basic level in that all discourse is constructed with language. The manipulation of language impacts how people interact and respond. Language and discourse are fluid, however, because they both shape and define the culture in which they are present. It is culture that provides much of the meaning for the language that happens within discourse.
Language contains clues about what should come next in a discourse. For example, if someone says "hello," that person generally expects the other person to say "hello" as well. At the very least, the first person wants an acknowledgement they have spoken, which the second person might give with a nod or other gesture. In this way, language controls some of the direction of discourse.
A main principle behind language and discourse is that, because language controls discourse direction to a large degree, people who learn how to control language learn how to manipulate discourse, as well. This is known as discourse management. By phrasing a question in a very specific way, for example, a person might force another person to respond in a particular way or even to stop the discourse altogether. Control of language thus is a tool for gaining and exercising power over others.
One important connection between language and discourse is that culture dictates language interpretation to a large degree. For example, if someone comes from a very religious Christian area, he might see it as irreverent if someone who isn't religious uses the phrase "my God" nonchalantly. This can lead to misunderstanding and conflict, hindering discourse and subsequent relationship building. Normally, evidence of the cultural beliefs that drive language and discourse is present elsewhere in a person's life.
Culture is always changing, and as a result, so is language. What is appropriate discourse at one time might not be appropriate in another time. An example is the use of words and phrases such as "swell" or "it's the bee's knees," which were popular in the 1950s but have fallen out of favor. Based on current interpretation of these words and phrases, a person might see another individual who used them in discourse as old-fashioned or outdated.
Gender also has a huge impact on language and discourse. For instance, in some cultures, women are seen as second-class citizens or the weaker sex. In these cultures, it sometimes is considered very rude for a woman to enter into a discourse without invitation from a man. In other cultures, more effort is taken to create gender equality through language and thereby encourage different rules of discourse engagement, such as the integration of gender neutral pronouns.
The connections between language and discourse mean that one cannot study language in depth without also studying discourse. Studying these areas, in turn, requires an understanding of cultural contexts. This is why linguistics is such a challenging field: meaning is not constant. Linguists are constantly trying to figure out exactly how language adapts and adjusts the rules of discourse.