A separable verb is a verb that is composed of a lexical core and a separable particle. In some sentence positions, the core verb and the particle appear in one word, whilst in others the core verb and the particle are separated.
In Chinese, verbs that can be separated usually follow the Verb + Object word order. For example, 念书 (niànshū) means to study, but 念 (to read, study) and 书 (book) are often separated and treated as two words within a sentence.
Not separating verbs is one of the most common mistakes English speakers make.