Formative Assessment is to monitor student learning to provide ongoing feedback that can be used by instructors to improve their teaching and by students to improve their learning. More specifically, formative assessments: help students identify their strengths and weaknesses and target areas that need work.
Summative Assessments are a mirror to student thinking. It help teachers and students see a trajectory of their learning. Teachers can use them to identify which students are ready for other tasks; and which students need more time to develop specific concepts.