The words "When he was like that" form a dependent clause. A dependent, or subordinate clause, is formed by a subject and a verb and starts with a subordinate conjunction (in this case, "when") or a relative prounoun. Also, a dependent clause does not express a full idea on its own. That is why it is dependent: it needs the information expressed by the main clause in order to make sense. For instance:
<em>When he was like that</em> (dependent clause), <em>the whole world seemed to cry with him</em> (main clause).
