Transition sentences are generally used in nonfiction, and more rarely in fiction or poetry. Their main function is to connect one paragraph to another. More generally, they also help an article, academic paper or essay flow from one idea to another. Without transition sentences, the connections between paragraphs and topics are less obvious. This makes the reader work harder than necessary to understand your piece.
When you're reading a published piece, you can often identify a transition sentence by looking for key words and phrases. Some common words you may run across include "because" or "however." Typical phrases might include "on the other hand" or "for example." Generally, a transition sentence comes at the very end of one paragraph and signals that a shift, contradiction or elaboration will be coming in the next paragraph. Sometimes, the first sentence of the next paragraph will also contain a transition element that helps link it to the previous paragraph.
Transitions don't have to be elaborate. In fact, they can be very brief. Making a smooth transition from idea to idea can be accomplished by writing something as simple as, "And yet, other experts disagree with this assessment."
Inexperienced writers often feel that transition sentences seem obvious, forced or formulaic. In your mind, it may be obvious how the first paragraph connects to the second paragraph. However, this is because the topic is one you have spent a lot of time researching. For the reader who is new to this material, these connections are less obvious, and a transition sentence is usually unobtrusive and yet very helpful.
If you have ever had a professor or editor say your writing felt "choppy" or "disconnected," your piece may have lacked sufficient transitions. Transition sentences help a reader anticipate shifts in the writing from one topic to another, or from one opinion to an opposing opinion. They also help a reader understand how one idea relates to another. Using transition sentences makes your writing flow smoothly and keeps your ideas coherently organized.