Jhn 16:21 A woman when she is in travail hath sorrow, because her hour is come: but as soon as she is delivered of the child, she remembers no more the anguish, for joy that a man is born into the world.
A wife, when she is in labor, has pain since her time is under way. However, when she has brought forth a child, no longer does she remember the suffering in the midst of the joy because a person has been brought forth into the world of people.
In the previous verse, the word translated as "sorrow" (lype) was translated in my alternative as "pain" because that translation better fit with the surrounding material. This verse strengthens that connection. It is pain not sorrow that is associated with childbirth.
The same Greek verb is translated as "is delivered" and "is born" in the KJV. This word is a casual form of a Greek word meaning "to be produced" and "to come into being." this is the verb Christ always used to refer to the "coming of the kingdom." The idea that our world, the temporal world, is the realm of becoming (coming into being) is a central theme of Christ's. So the birth of a child is a specific metaphor for the coming of the kingdom. This is why "birth" is so central to the Christ story. It is a tale of becoming.
Christ usually uses the word translated as "world" (kosmos) in a critical way, referring to the "world order", that is, the temporal powers-that-be who oppose the kingdom. This verse is unusual in that Christ uses the same word is a positive way, as the world in which a child can find a place. This reminds us that the world order though short-sighted and selfish is not always bad: it is the place in which we embrace each other.
There is a connection here between the birth of a child and the birth of the kingdom.
τίκτῃ (2nd sg pres ind mp) "She is in travail" is from (tikto), which means "to bring into the world", "to beget" (of the father), "to bring forth" (of the mother), and (of animals) "to breed" or "to bear young". As a metaphor, it was used to mean "to generate", "to produce, and "to engender,"
ἔχει "Has" is from echô (echo), which means "to have", "to hold", "to possess", "to keep", "to have charge of", "to maintain", "to hold fast", "to bear", "to keep close", "to keep safe," and "to have means to do."
ἦλθεν (3rd sg aor ind act) "Is come" is from erchomai (erchomai), which means "to start," "to set out", "to come", "to go," and any kind of motion. It means both "to go" on a journey and "to arrive" at a place.
ὥρα "Hour" is from hora. which means "any period", "season," (especially springtime), "year' (generally), "climate" (as determined by seasons), "duration", "the twelve equal parts into which the period of daylight was divided", "the fitting time" (for a task).
αὐτῆς "Her" is from autos (autos), which means "the same," and the reflexive pronouns, "myself", "yourself", "himself", "herself", "itself," or the oblique case of the pronouns, "him", "her," and "it." It also means "one's true self," that is, "the soul" as opposed to the body and "of one's own accord."
γεννήσῃ (3rd sg aor subj act) "Is delivered" is from gennaô (gennao), which means "to beget", "to bring forth", "to produce from oneself", "to create," and "to engender." this is the causal form of gignomai, which is translated as "done" in the NT, but which comes closer in meaning to "become."
ἐγεννήθη (3rd sg aor ind pass) "Is born" is from gennaô (gennao), which means "to beget", "to bring forth", "to produce from oneself", "to create," and "to engender." this is the causal form of gignomai, which is translated as "done" in the NT, but which comes closer in meaning to "become."
εἰς "Into" is from eis (eis), which means "into (of place)," "up to (of time)", "until (of time)", "as much as (of measure or limit)", "as far as (of measure or limit)", "towards (to express relation)", "in regard to (to express relation)", "of an end or limit," and "for (of purpose or object)."
κόσμου "World" is from kosmos, which mean "order", "good order", "ruler", "world order", "universe," and "the world of men." Matthew uses it when Christ is talking about the order in the universe, specifically the order of the world of men, as it is designed to be.