You use in the world to emphasize a statement that you are making.
come down in the world
to have less money than you had before and now have a lower social status
come up in the world
to have more money than you had before and now have a higher social status
in a world of one's own
If you say that someone is in a world of their own , you mean that they seem not to notice other people or the things going on around them.
go/come up/down in the world
If you say that someone has gone up in the world , you mean they have become richer or have a higher social status than before. If you say they have come down in the world , you mean they have become poorer or have a lower social status.
in an ideal/a perfect world
You can use in an ideal world or in a perfect world when you are talking about things that you would like to happen , although you realize that they are not likely to happen.
with the best will in the world
even with the best of intentions
what in the world/who in the world/where in the world
You can use in the world in expressions such as what in the world and who in the world to emphasize a question , especially when expressing surprise or anger .