In Spanish, it is very common for the subject to not be explicitly stated, although it is implied by the conjugation of verb. For example, the word hablamos, which means "we speak," can be a complete sentence. The subject of the sentence is not explicitly stated, although it is implied to be nosotros, which means "we."

In English, the subject can be similarly implied, although only when the verb is in the imperative mood, that is, when the sentence is a command. For example, the command "speak" is a complete sentence; the listener can infer that the subject is "you."

Exclamations, such as "ouch!" in English or "¡ay!" in Spanish can express a complete thought, although they generally are not considered to be sentences.

Term in Spanish: oración, frase

Examples in Spanish: El cielo es azul. ¿Cuál es el significado de la vida? ¡Callate! (These sentences make a statement, ask a question and give a command, respectively.)

Examples in English: The sky is blue. What is the meaning of life? Shut up! (These sentences make a statement, ask a question and give a command, respectively.)

Related Resources:

Word Order
Spanish is more flexible than English is in the way that words can be arranged in a sentence.

10 Mistakes to Avoid While Learning Spanish
Among other things, don't always assume that Spanish sentences are structured the same as English ones.