The Seven Deadly Sins are sins that characterize fallen humanity, so classified by traditional orthodox Christianity and especially held to, and taught by, the Roman Catholic Church since the early Middle Ages. Protestants would agree that the seven vices on the list are sins, but generally don't make a distinction between mortal and venial sins in the same way Catholics do.
The Seven Deadly Sins in the Bible
The Bible includes lists of sins, though none align exactly with the traditional "seven deadly" sins.
In the Old Testament, Proverbs 6:16-19 reads,
“These six things doth the LORD hate: yea, seven are an abomination unto him: 17 A proud look, a lying tongue, and hands that shed innocent blood, 18 An heart that deviseth wicked imaginations, feet that be swift in running to mischief, 19 A false witness that speaketh lies, and he that soweth discord among brethren.”
The only direct parallel between this list and the traditional list of seven seems to be “pride,” although there are other loose associations as well.
In the New Testament, Galatians 5:19-20 says:
“Now the works of the flesh are manifest, which are these; Adultery, fornication, uncleanness, lasciviousness, 20 Idolatry, witchcraft, hatred, variance, emulations, wrath, strife, seditions, heresies, envyings, murders, drunkenness, revellings, and such like: of the which I tell you before, as I have also told you in time past, that they which do such things shall not inherit the kingdom of God.”
Because this passage says that those who commit these sins shall not inherit the kingdom of God, these are traditionally classified as “mortal sins.”
History of the Seven Deadly Sins
"The Seven Deadly Sins" can be traced back to the 4th century when a monk named Evagrius Ponticus generated a list of sins, likely stemming from problems he saw in his own day. 
His list included the following sins: gluttony, fornication/prostitution, greed, pride, sadness (i.e. envy – sadness at another’s good fortune), wrath, boasting (i.e. a verbal proclamation of inner pride), and dejection (i.e. gloominess, depression). Evagrius' list proved to have staying power in the Church and was translated from Greek into Latin and used for educational and devotional purposes.
In 590 Pope Gregory I revised Evagrius’ list, although the essence remained the same. Gregory’s list included sloth (a combination of three of the sins on Evagrius’ list), greed, pride, lust, gluttony, wrath, and added envy. Gregory also emphasized an order to the list: (1) lust, (2) gluttony, (3) greed, (4) sloth, (5) wrath, (6) envy, and (7) pride. 
Gregory’s list, and its order, was cemented into Roman Catholic tradition for centuries to come when the Italian poet Dante Alighieri (1265-1321) used them in his epic tale, The Divine Comedy.