Hajimemashite means "How do you do?" or "Nice to meet you." This is the very first phrase you say when meeting someone new for the first time. It literally means "For the first time." It's always used as an introduction. For example, "はじめまして。田中と申します。" (How do you do? My name is Tanaka.).

初めて人に会う時に言う挨拶です。自己紹介の最初に使います。「はじめまして！」