What is the meaning of "baptism by fire"? We all know what water baptism and baptism by the Holy Spirit are. But what does John the Baptist mean by, "He will baptize you with the Holy Spirit and FIRE" in Luke 3:16:


  John answered and said to them all, "As for me, I baptize you with water; but One is coming who is mightier than I, and I am not fit to untie the thong of His sandals; He will baptize you with the Holy Spirit and fire." (emphasis added)


Is there a generally-accepted interpretation of what fire means in this context; or can there be a quick overview of the most-accepted understandings?
16 John answered, saying unto them all, I indeed baptize you with water; but there cometh he that is mightier than I, the latchet of whose shoes I am not worthy to unloose: he shall baptize you in the Holy Spirit and in fire:
  
  17 whose fan is in his hand, thoroughly to cleanse his threshing-floor, and to gather the wheat into his garner; but the chaff he will burn up with unquenchable fire.


According to the context in “fire” in 3:16 and 17 is not the fire in Acts 2:3, which is related to the Holy Spirit. 


  3 And there appeared unto them tongues parting asunder, like as of fire; and it sat upon each one of them.


Also, the same incident can be seen in Matthew 3:10 and 11. John the Baptist said:


  10 And even now the axe lieth at the root of the trees: every tree therefore that bringeth not forth good fruit is hewn down, and cast into the fire.
  
  11 I indeed baptize you in water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you in the Holy Spirit and in fire:


These verses mention fire twice. It is not logical to say that the first time fire is mentioned it is negative, but the second time the same word is used it is positive. Therefore, baptism in fire does not have a positive meaning; it is not related to the baptism in the Holy Spirit. 

Rather, it is the fire in the lake of fire (Rev. 20:15). 

Matthew Henry:


  Probably this refers to the destruction of Jerusalem by the Romans, which was not, as other judgments had been, like the lopping off of the branches, or cutting down of the body of the tree, leaving the root to bud again, but it would be the total, final, and irrecoverable extirpation of that people, in which all those should perish that continued impenitent. Now God would make a full end, wrath was coming on them to the utmost.


Commentary Critical and Explanatory on the Whole Bible (1871)


  The "fire," which in another verse is called "unquenchable," can be no other than that future "torment" of the impenitent whose "smoke ascendeth up for ever and ever," and which by the Judge Himself is styled "everlasting punishment" ( Matthew 25:46 ).
  Verse 12 continues:
  
  Whose winnowing fan is in His hand. And He will thoroughly cleanse His threshing floor and will gather His wheat into His barn, but the chaff He will burn up with unquenchable fire.


If a person is wheat, Christ will baptize him with the Holy Spirit, and he will have life. However, if he is chaff, He will baptize him with fire; that is, He will put him into the lake of fire. 

Here, it means that if the people will truly repent and believe in the Lord Jesus, the Lord will baptize them in the Holy Spirit so that they may have eternal life. Otherwise, the Lord will baptize them in fire, putting them into the lake of fire for eternal punishment. John’s baptism was only for repentance, to usher people to faith in the Lord. The Lord’s baptism is either for eternal life in the Holy Spirit or for eternal perdition in fire.

So, the Pharisees and Sadducees, came to John the Baptist in a pretentious way. It is as if John said, “If you do not bear fruit, you will be cut down and cast into the fire. You may fool me because I come only to baptize you with water, but you cannot fool Him. When He comes, He will baptize with the Holy Spirit and with fire. He will clear up His threshing floor. If you are the real ones, He will baptize you with the Holy Spirit for life. If you are the false ones, He will put you into the fire.”

Lastly, there are three kinds of baptisms referred in the Bible: the baptism in water, the baptism in the Holy Spirit, and the baptism in fire. The baptism in water is for repentance, the baptism in the Holy Spirit is for life, and the baptism in fire is for perdition.