I am only a learner, and there will be multiple posts with additional reasons and instances where the circumflex is used, but here are 3 that comes to mind first.
1) It makes the vowel "closed" (for "o" and "e").
"avó" (open, meaning grandmother) as opposed to "avô" (closed, meaning grandfather)
2) For words of Greek origin, it tells you where the stress falls on.
economia (stress falls on the usual place, penultimate)
econômico (moved to the second "o")
ciência (it's out of place at "e")
3) There are some orthographic differences between European Portuguese and Brazilian Portuguese. If I am not mistaken, in Brazilian Portuguese, they use the circumflex, and acute accent in European Portuguese.
"quilómetro" (EP) while "quilômetro" (BP)