As a part of speech, the conjunction is said to join elements of a sentence, but we should remember that join means here to bring into some kind of relationship, whether that is to connect (as in, birds and squirrels) or to separate (as in, not in the tree but on the grass). Connecting and separating, associating and disassociating, is the gearbox of rationality, and generates the power of the language we write and speak every day.
Conjunctions are organized into two large groups, coordinating and subordinating, and the conjunctions within each group take on a specific logical role. Some, like and, are called additive conjunctions, because they increase the number of things seen to be related: I saw birds and squirrels in the tree. Other conjunctions, like but, are called adversative, because they contrast certain ideas: The squirrels were not in the tree but on the grass. And still others, like if, are called conditional, because they predicate a circumstance in which something else may or may not be true: If the squirrels were in the tree, the birds were on the grass.
Two conjunctions that are worth our attention for matters of style and punctuation are the adversatives but and however. These conjunctions, like all the others, can join nouns to nouns, phrases to phrases, and clauses to clauses, but it is in this last configuration that practical problems of composition often arise. In the sentence The grass needs to be cut, but the lawnmower is broken, the conjunction but is contrasting, or putting into some kind of opposition, the assertions of the two clauses (notice that a comma almost always precedes but when it joins two clauses). The two clauses are brief and uncomplicated, and so the simple monosyllable but does the job nicely.
If I expand the two clauses, though, and complicate the situation a little, I have the opportunity to use another adversative conjunction, however. Notice in particular the punctuation: There’s no doubt that the grass needs to be cut; however, the lawnmower I just bought won’t start. Because the adversative however is generally used to contrast longer, more involved ideas, it requires that the two contrasting clauses be separated by a semicolon (not a comma), and that a comma follow the conjunction. It is extremely common to see a comma here where the semicolon is required, but there is no way grammatically to justify that because the construction results in a run-on sentence. (This is explained in more detail in an earlier post, Running On and On.)
If I now choose to expand the statement even a little more, I can place the conjunction not at the head of the second clause, but somewhere within it. In this design, called a postpositive construction (postpositive derives from the Latin meaning put after), I isolate the conjunction with a pair of commas: There’s no doubt that the grass needs to be cut; the problem, however, is that the expensive lawnmower I just bought won’t start. This construction raises what is called the diction of the statement, the choice of words that produce a style appropriate to the audience and purpose at hand. By delaying the appearance of the conjunction, which is the signal of the logic, the reader is briefly held in suspense as to what the connection between the two clauses really is, and this uncertainty draws them more attentively into the run of the ideas.
Conjunctions are integral to the design of our sentences, particularly as we associate clauses one to the next and compose a context of ideas. The conjunctions we choose in joining clauses depend first on the logical connection we want to show, and then on the style of the document we are writing. The finish, as is ever the case with language, lies in such details of arrangement and punctuation.