Argumentative writing is designed to pose a claim and support for the claim using persuasive arguments. Such writing becomes more effective when conjunctions make the points flow smoothly. Conjunctions connect words or phrases together, making a text easier to read. Transitions function the same way -- by unifying a whole piece of writing.
Function
Conjunctions serve as a cue within a sentence, signaling the reader that another idea is coming. Coordinating conjunctions link ideas by showing how they relate. For example, a word like "and" indicates two ideas go together. A subordinating conjunction indicates that one idea depends on another. For instance, in this sentence the word "unless" depends on the action that follows it: We will be late unless we leave now. Correlative conjunctions join elements within a sentence, indicating the two are of equal importance. The words "neither" and "nor" work this way in this sentence: I like neither carrots nor celery.
Transitions
Transitions serve the same purpose as conjunctions, but on a larger scale. They signal to the reader the relationship between ideas in a paragraph or even between paragraphs. By connecting larger ideas, they let readers know what to do with the information presented to them. Indicating these connections helps reinforce the argument within a paper. Phrases like "for example" let the reader know the information that follows is meant to support an idea. Thus, the use of transitions cues readers into the writer's thinking process.
Cohesion
Conjunctions improve the paper as a whole by giving the writing coherence, or flow. A conjunctive adverb such as "however" or "overall" joins two complete sentences, using either a semicolon or a period. These words and phrases serve different purposes: showing agreement, opposition, causality, support or emphasis, consequence and conclusion. They work like a bridge from one of the writer's points to another. For example, "however" lets the reader know the statement that follows is in opposition to the preceding; "overall" signals a conclusion. These signals guide readers to either reflect on what came before or anticipate what is coming next in the paragraph.
Importance
Conjunctions and conjunctive adverbs unite elements of an argument together. When the argument is unified and cohesive, readers are more likely to believe what the writer is saying. Readers need a guide; without this guide, they might get lost in the argument. Readers struggling to follow a writer's thought progression become frustrated and may even stop reading the paper. When a writer takes the time to make the argument more readable, this engenders faith and goodwill in the readers. As Aristotle pointed out, creating that goodwill, what he called ethos, makes people more open to persuasion.