allow

Compared meaning: to let someone do something (verb).

比较义项：允许某人做某事，或允许某事发生（动词）。

• let

  Informal and conversational; followed directly by a bare infinitive (let sb do sth, never to do), and often describes tolerating or allowing something to happen rather than formally approving it.

  非正式、口语化；后面直接接不带 to 的动词原形（let sb do sth，而非 to do），且常表示听任某事发生，而不是正式批准。

  My parents let me stay out late last night.

  昨晚我父母让我在外面待到很晚。

• allow 本词

  Neutral in register, common in both speech and writing; uses the pattern allow sb to do sth, and is the usual choice for rules or permissions set by a person in authority.

  语气中性，口语和书面语都常用；句型为 allow sb to do sth（宾语后接 to 不定式），是描述权威人物或规则所给许可时最常用的词。

  The teacher didn't allow phones during the final exam.

  老师在期末考试期间不允许使用手机。

• permit

  Formal, often official or legal in tone, typical of written rules and regulations; also uses permit sb to do sth, but sounds stiff or overly formal in casual personal situations.

  语气正式，常带有官方或法律色彩，多见于书面规则和法规；句型也是 permit sb to do sth，但用在日常私人场合会显得生硬、过于正式。

  The city council will not permit new construction near the river.

  市议会不会准许在河边附近新建建筑。

Let, allow, and permit all mean to give permission, but formality differs. Let is informal, followed by the base verb, as in let someone go. Allow is neutral, common in speech and writing. Permit is formal, for written rules. Not compared: permit as a document.

这三个词在“允许”这个意义上很接近，但正式程度不同：let 最口语化，allow 中性通用，permit 最正式，常见于官方或书面语境。这里不比较 permit 作名词时的“许可证”义，也不比较 let 的“出租（房屋）”等其他义项。