A stated best guess, offered as a guess. An estimate becomes dangerous the moment it is quoted as a measurement.
Latin aestimare (to value, to appraise), originally the assessing of a thing's worth in a legal or financial reckoning; the sense widened over time from appraising a specific value to approximating any quantity at all.
Its root was a legal appraisal of worth, not a casual guess: aestimare named the formal assessing of what something was worth before a court or a market. An estimate still carries that old weight even offered lightly, which is why it turns dangerous the moment it gets quoted as settled.