Portuguese (Brazil) · Pronunciation Guide
oo MAYSS. The circumflex specifies a closed vowel — a tight "ay," not the open "eh" of "bed."
A monosyllable, so the circumflex isn't placing stress — it's locking in the closed vowel, which would otherwise be ambiguous. The plural is "meses," where the accent disappears because the word now ends in -es and the default rule takes over, putting the weight on the second-to-last syllable anyway.
Listen: o mês
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Este mês foi difícil.
This month was hard.
Listen: Este mês foi difícil.
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"Este mês foi difícil" links "este mês" so the raised final "ee" of the demonstrative runs into the m. "Difícil" then ends the sentence on a vocalized l, and its opening di is palatalized to "djee" — so the sentence has a palatal at both ends and a glide in the middle.
Using an open "eh" gives "MESS," which is the wrong vowel quality. The circumflex is telling you to keep it tight. Learners also drop the accent in writing, which is a genuine spelling error, and they forget that the plural loses it — writing "mêses" is wrong.