In modern usage, swearing and profanity is defined as using any vulgar language. The Biblical definitions are slightly different.
From the 10 Commandments:
Exo 20:7 “You shall not take the name of the LORD your God in vain, for the LORD will not hold him guiltless who takes His name in vain.
Taking God’s name in vain was a serious sin. For this reason, even today many Jews refrain from writing “God” or “Yahweh”. The web site Jewishworldreview.com changes all references to God into “G-d”. To profane God’s name (to take God’s name out of the temple) was a sin. This is a really important point. It would be wrong to conflate “using course words” with “taking God’s name in vain”. To do so would be, itself, profaning God’s name. It would be saying God’s name is on par with coarse language. The Biblical sin of profanity is limited to only God’s name.
Another prohibition is against swearing. Swearing is not vulgar language in the Biblical context. Instead it is placing oaths on propositions using the name of God. In the Bible, Israel was notorious for swearing oaths. An example:
Gen 24:3 and I will make you swear by the LORD, the God of heaven and the God of the earth, that you will not take a wife for my son from the daughters of the Canaanites, among whom I dwell;
In the Old Testament, swearing was allowed, conditionally:
Lev 19:12 And you shall not swear by My name falsely, nor shall you profane the name of your God: I am the LORD.
God even swears on His own name:
Gen 22:16 and said: “By Myself I have sworn, says the LORD, because you have done this thing, and have not withheld your son, your only son—
Gen 22:17 blessing I will bless you, and multiplying I will multiply your descendants as the stars of the heaven and as the sand which is on the seashore; and your descendants shall possess the gate of their enemies.
But when Jesus came, it seems God had grown tired of all the false swearing on His name. The prohibition seems to have been expanded to preclude false swearing altogether. Jesus is not overturning the previous law, but he is expounding on it. Instead of swearing by God’s name, people were to refrain from swearing entirely. Jesus says “Let your yes be yes and your no be no”:
Mat 5:33 “Again you have heard that it was said to those of old, ‘You shall not swear falsely, but shall perform your oaths to the Lord.’
Mat 5:34 But I say to you, do not swear at all: neither by heaven, for it is God’s throne;
Mat 5:35 nor by the earth, for it is His footstool; nor by Jerusalem, for it is the city of the great King.
Mat 5:36 Nor shall you swear by your head, because you cannot make one hair white or black.
Mat 5:37 But let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No.’ For whatever is more than these is from the evil one.
This is reiterated by James:
Jas 5:12 But above all, my brethren, do not swear, either by heaven or by earth or with any other oath. But let your “Yes” be “Yes,” and your “No,” “No,” lest you fall into judgment.
Presumably, this would lead to Israel being more truthful in general. If the only time a promise were to be fulfilled was during swearing, that creates a vacuum for abusing normal promises. Jesus and James were promoting truthfulness without swearing (not necessarily saying swearing is immoral). Jesus and James were also protecting God’s name.
1Ki 16:11 And it came to pass, when he began to reign, as soon as he sat on his throne, that he slew all the house of Baasha: he left him not one that pisseth against a wall, neither of his kinsfolks, nor of his friends.
The Bible has all kinds of crude language. In 1 Kings 16, a coarse illustration is given to mean “men”. The phrase is “he left him not one that pisseth against a wall” which refers to someone with the proper organs to stand while peeing. This is a crude way to say “men”. The New King James translators cover the idiom and just translate it “men” (a bad translation practice).
While crude language is not necessarily wrong, Paul warns against it:
Eph 4:29 Let no corrupt word proceed out of your mouth, but what is good for necessary edification, that it may impart grace to the hearers.
This might not be particularly against solitary words, such as modern swear words. Instead the idea seems to be not to communicate flasehoods or evil. The word is logos and has a host of meanings. In Matthew 28:15 it means a particular “series of sentences” even though the word is singular:
Mat 28:15 So they took the money and did as they were instructed; and this saying is commonly reported among the Jews until this day.
But Paul’s statement can be extended to single swear words. But the real question is “Do those swear words edify?” The answer might not always be “no”.
Other verses used to condemn swear words are:
Col 3:8 But now you yourselves are to put off all these: anger, wrath, malice, blasphemy, filthy language out of your mouth.
Jas 3:9 With it we bless our God and Father, and with it we curse men, who have been made in the similitude of God.
Jas 3:10 Out of the same mouth proceed blessing and cursing. My brethren, these things ought not to be so.
Psa 34:13 Keep your tongue from evil, And your lips from speaking deceit.
These are not necessarily against course word usage, although they can be taken as such. The principle that instead seems to be stressed is general communication. Coarse words are on par with course sentences.
What this should tell Christians, is that although general avoidance of vulgarity is good, it is not necessarily a sin to use coarse language.