Where does the word nativity come from?

The word derives from the Latin 'natal' meaning birth (1200–50; ME nativite < OF nativité < LL nātīvitās)

Nativity scene in Barcelona

Natal is also the source of several other English words, including native and nature.

While pre-natal is the standard medical term and in common use, nativity is almost exclusively used in the religious/iconic sense, defined in the Oxford Dictionary as follows: 
the birth of Jesus Christ/a picture, carving, or model representing Jesus Christ’s birth

What is the cultural significance of the Nativity?

The Nativity is the best known story in the Christian tradition. The key elements are: 
  • the baby Jesus, Mary & Joseph
  • the Shepherds
  • the Magi/Wise Men/Three Kings
  • the manger 
The Nativity is a unifying symbol for Christians across the world. In Ron Gainer's An Australian Carol, emigrants to the New World remember their home land through the image of the Nativity:

So joyously pray/Christ the Saviour was born on this day.

Do Christians agree on the meaning of the Nativity?

The Nativity the subject of theological debate:

The Nativity, refers to the accounts of the birth of Jesus, primarily based on the two accounts in the gospels of Luke and Matthew, and secondarily on some apocryphal texts. The word is anglicized from Latin De nativitate Iesu, a section title in the Vulgate.

The ... gospels of Luke and Matthew describe Jesus being born in Bethlehem, in Judea, to a virgin mother. Luke features the Christmas story, in which Joseph and Mary, as part of a census, travel to Bethlehem, where Jesus is born and laid in a manger.

Angels proclaim him a saviour for all people, and shepherds come to adore him. In Matthew, wise men follow a star to Bethlehem to bring gifts to Jesus, born the King of the Jews. King Herod massacres all the toddler boys in Bethlehem to kill Jesus, but the holy family flees to Egypt and later settles in Nazareth. 

Scholars debate whether these two accounts can be reconciled or not, and some view the narratives as non-historical. Source

A Paul McCartney story about the young John Lennon's late night encounter with a Nativity scene inspired this fun Fred & Rita playscript.