While “什么时候” is a functional phrase without deep philosophical meaning, its usage reflects an important aspect of Chinese grammar and communication. In English, “When” is typically placed at the very beginning of a question (“When are you going to the store?”). In Chinese, “什么时候” is placed where the answer would logically go in a statement. This follows the standard Subject-Adverbial(Time)-Verb-Object sentence structure.
This structural difference is a key insight into Chinese grammar. You aren't rearranging the sentence to ask a question; you are simply substituting the “time” part of the statement with the “what time” question phrase. It's a simple, elegant system.
“什么时候” is used constantly in all aspects of modern life. It's a neutral term, appropriate for both formal and informal situations.
Its meaning is always direct and clear. The context is determined entirely by the rest of the sentence.