What is not generally realized, is that this phrase, taken in context, is referring to a specific event revealed in Bible Prophecy as a horrific event that will cause much weeping--an event that will pass. After that, the weeping will be replaced with joy.
The entire verse says this: For his anger endures but a moment In His favor is life Weeping may endure for a night but joy comes in the morning
Psalm 30:5 begins by referring to the anger of the Lord and how it lasts but a moment (a very brief-limited period of time). The weeping, in this verse, is a direct reference to his anger, and for the length of time that the anger and the weeping is given. It will be for a night.
How does one get Bible prophecy from this verse? By comparing it with other verses that are directly connected with this one. Below are only two examples, but there are many more.
Isaiah 26:20-21 reveals that a time is coming when the Lord will come "out of his place" to punish the inhabitants of the earth. Isaiah reveals that his indignation (anger/wrath) will last only for a "moment." (same Hebrew word used in Psalm 30:5. Your Bible doesn't say "moment?" --a little "while" and a moment are not the same thing, and the evidence weighs heavily in favor of the manuscripts the King James Bible was translated from)
John 9:4 Jesus makes the statement: I must work the works of him that sent me while it is day for the "night" comes when no one can work.
In each of the above verses, both Jesus and Isaiah are referring to a specific period of wrath that is coming on the inhabitants of the earth. Joel referred to this time as a dark and a cloudy day (Joel 2). Jeremiah calls it "The Time of Jacob's Trouble." Jesus also called it a time of "Great Tribulation."
Thank God this terrible time that has not yet arrived. In the meantime, we must be about our Father's business in sharing the good news of Jesus, the only Christ--God's Christ--who came and, through the blood of his cross, made peace with God for us.
Right now, we live in the time of favor (1 Corinthians 6:2). We can call upon the name of the Lord to be saved (Romans 10:9-10,13). But during the time of indignation, only those who "endure to the end" will be saved (Matthew 24:13).