The phrase "the time of Jacob's trouble" is a quote from Jeremiah 30:7 “Alas! for that day is great, so that none is like it: it is even the time of Jacob's trouble, but he shall be saved out of it.”
In the previous verses of Jeremiah 30, we find that the Lord is speaking to Jeremiah the prophet about Judah and Israel (30:3-4). In verse 3, the Lord promises that one day in the future, He will bring both Judah and Israel back to the land that He had promised their forefathers. Verse 5 describes a time of great fear and trembling. Verse 6 describes this time in a way that pictures men going through the pains of childbirth, again indicating a time of agony. But there is hope for Judah and Israel, for though this is called "the time of Jacob's trouble" the Lord promises He will save Jacob (referring to Judah and Israel) out of this time of great trouble (verse 7).
“Alas! for that day is great, so that none is like it: it is even the time of Jacob's trouble, but he shall be saved out of it.” Jeremiah 30:10-11
Also, the Lord says He will destroy the nations who held Judah and Israel in captivity, and He will never allow Jacob to be completely destroyed. However, it should be noted that the Lord describes this as a time of discipline for His people.
“For I am with thee, saith the Lord, to save thee: though I make a full end of all nations whither I have scattered thee, yet I will not make a full end of thee: but I will correct thee in measure, and will not leave thee altogether unpunished.”Jeremiah 30:11
"Alas! for that day is great, so that none is like it: it is even the time of Jacob's trouble, but he shall be saved out of it.” Jeremiah 30:7
The only time period that fits this description is the period of the Tribulation. This time is unparalleled in history.
Jesus described the Tribulation using some of the same imagery as Jeremiah. In Matthew 24:6-8, He stated that the appearance of false christs, wars and rumors of wars, famines, and earthquakes are "the beginning of birth pains."
Paul, too, described the Tribulation as birth pains. “For when they shall say, Peace and safety; then sudden destruction cometh upon them, as travail upon a woman with child; and they shall not escape." 1 Thessalonians 5:3
This event follows the Rapture and the removal of the Church, in 1 Thessalonians 4:13-18. Paul reemphasizes the absence of the Church from this time period by saying, "For God hath not appointed us to wrath, but to obtain salvation by our Lord Jesus Christ," 1 Thessalonians 5:9. The wrath spoken of here is God's judgment on the unbelieving world and His discipline of Israel during the Tribulation.
These “birth pains” are described in detail in Revelation 6-12 Part of the purpose of the Tribulation is to bring Israel back to the Lord.
For those who have received Christ as Savior from sin, the time of Jacob's trouble is something for which we should praise the Lord, for it demonstrates that God keeps His promises. He has promised us eternal life through Christ the Lord, and He has promised land, seed, and blessing to Abraham and his physical descendants. However, before He fulfills those promises, He will firmly discipline the nation of Israel so that they return to Him.