Way back in high school, an English teacher asked me if I understood how I was using the word "for" in one of my sentences. I didn't, and I took it as a criticism. Since that day, I have shied away from using "for" in this way. Today, I ran across a sentence that uses it in that way: "So if you are happy to close-mike a source, don't discount using an omni, which will often sound less coloured than a cardioid, for the spill penalty will probably be negligible." Can someone please tell me if and why this use of "for" is correct?
It is correctly used.
It is different than most uses of for because it functions as a conjunction instead of as a preposition.
The meaning is, obviously, because/since/as as Janus Bahs Jacquet states in his comment to the question.
The following definition and (especially the first parts of the) usage note will likely be of interest to you:
. . .
Usage Note: For has been used as a conjunction meaning "because, since" for over 1,000 years. It is familiar in many famous quotations, from the New Testament's beatitudes (Blessed are the meek: for they shall inherit the earth, Matthew 5:05) to Shakespeare's sonnets (For thy sweet love rememb'red such wealth brings / That then I scorn to change my state with kings). Today this use of for is rare in speech and informal writing, and it often lends a literary tone or note of formality.
Like the word so, for can be viewed as either a subordinating or a coordinating conjunction, and it has been treated variously as such. It has the meaning of a subordinating conjunction, since it clearly subordinates the clause that follows it to the previous clause or sentence. But like a coordinating conjunction, for has a fixed position in the sentence, and its clause cannot be transposed to precede the superordinate clause containing the main idea. It is ungrammatical in present-day English to say For they shall inherit the earth: blessed are the meek. Perhaps because of this ambiguity in function, for is treated variously with regard to punctuation. Sometimes it begins a dependent clause and follows a comma, and sometimes it begins an independent clause (as if it were a conjunctive adverb like moreover) and follows a semicolon or period (when it is capitalized as the first word of a new sentence). All treatments are acceptable in standard usage. The difference is really one of emphasis: starting a new sentence with for tends to call more attention to the thought that it introduces.
This is a good dictionary definition. Read the whole of it.