The most common and most likely answer to this crossword clue is the 10 letter word CONTINENTS
I've seen this crossword clue in The Times
C
O
N
T
I
N
E
N
T
S
Buddy explains!

The straight part
We know that "Parts of the world" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case parts of the world = continents.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CONTINENTS mean?
CONTINENTS noun- Each of the main continuous land-masses on the earth's surface, now generally regarded as seven in number, including their related islands, continental shelves etc.
- A large contiguous landmass considered independent of its islands, peninsulas etc. Specifically, the Old World continent of Europe–Asia–Africa. See the Continent.
- Land (as opposed to the water).