Unfortunately, this depends a lot on context. It could be the omission of a noun if used literally, but it almost never is. The sentence "Take a second." would normally be the omission of a prepositional phrase. The idiom is normally "take a second to..." It usually references thinking or actively sensing, i.e. "take a second to think through the problem before using brute force." Other phrases like this are "take a minute" or "take a moment" and have the same meaning. It does suggest something momentary though, as opposed to the related "take a while."
Interestingly, if someone says that something will take a second, you can expect them to be done shortly, but not literally in a second. If somebody will take a while, do not expect them to be done soon. These declarative (stating facts about the world) meanings carry through to the imperative (requesting or ordering that something be done) meanings as well.