입니다 is for stating something, mostly for declarative sentences while 입니까 is for interrogative sentences, I guess.

입니다 - It is .... (making a statement) 입니까 - Is it ...? (asking a question) Usually for the 아/어/여요 form simply changing your intonation is enough. However, this formal ending replace 다 with 까 in questions. Ex. Very formal "How are you?" 안녕하십니까?

When we make simple sentences, we use 입니다. Ex. 나는 학생입니다 나는 선생님입니다. When we make questions, we use 입니까. Ex. 학생입니까? 선생님입니까?