We use "그리고" to connect two sentences. It means that you want to add more information to the first sentence in a similar context. Also, we use "그리고" to show the time order of two or more events.
"그는 여동생이 있다. 그리고 그녀는 아주 귀엽고 예쁘다." is "He has a sister. And she is very cute and pretty.", "나는 샤워를 했다. 그리고 아침밥을 먹었다." is "I took a shower. And I had a breakfast."