The main New Testament word for “world” is the Greek “kosmos.”

It had the idea of something orderly, even beautiful, and is used in passages like Mtt 4:18. and Mtt 5:14. We moderns associate kosmos with the entire universe, and I think this New Testament word may overlap many of our ideas of the universe or kosmos. The general Hebrew equivalent would be ezret, which can be used for either land, or a country, or the “earth.”

It carries with it the idea of all mankind,

“… God so loved the world, that he gave his one and only Son, that whoever believes in him should not perish, but have eternal life.”
Jn 3:16 WEB

The word for an age is often translated as “world.”

The Greek word is ai?n, and it is variously translated as age, ages, time, eternity, forever, etc., or even “world.” Satan is spoken of as the “god” of this world, 2Cor 4:4, that is to say, god of this age. It speaks in Mtt 13:22 of a man being overcome with the cares and worries of this world, that is to say, the cares and worries of this age.

“Since the world began it has never been heard of that anyone opened the eyes of someone born blind. ”
Jn 9:32 WEB

Since this age began. Also we are told to not copy this age.

“Don’t be conformed to this world, but be transformed by the renewing of your mind, …”
Rom 12:2 WEB

This age thinks it is smart, but long range, they are not.

“Where is the wise? Where is the scribe? Where is the lawyer of this world? Hasn’t God made foolish the wisdom of this world?”
1Cor 1:20 WEB.

A final word that is used is for the inhabited world

When Luke tells the story of Jesus temptation, he says that Satan “showed him all the kingdoms of the world in a moment of time.” Lk 4:5 WEB, and the world translated “world” here is oikoumen?, and this Greek word means the inhabited world. Oikoumen? is used of preaching of the gospel to the entire world in passages like Mtt 24:14. Or again is speaks of Caesar Augustus having a census of the inhabited world in Lk 2:1. The general Hebrew equivalent to oikoumen? is tebel, which is often translated as “world.” Many Old Testament prophesies of the end of the age use both the words ezret earth, and tebel world.

But the main word of the New Testament is “kosmos”

Christians are the light of the world, Mtt 5:14. The field in which we are work is the entire world. “the field is the world;” Mtt 13:38. Or again,

“For what will it profit a man, if he gains the whole world, and forfeits his life? Or what will a man give in exchange for his life?”
Mtt 16:26 WEB

Especially since this world is soon to pass away.

“The world is passing away with its lusts, but he who does God’s will remains forever.”
1Jn 2:17 WEB

The world here is kosmos, and forever is ai?n.

WEB is the World English Bible, a copyright free revision
of the original ASV American Standard Version 1901