Formative assessment is an assessment that is strictly used to monitor a student's learning and give student feedback for improvement. Formative assessments include basically everything that is not a summative assessment that serves to tell an educator where the class is in regards to the material. Formative assessments include homework, entrance and exit tickets, cold calling, popcorn sharing, very minor quizzes, and even just listening to groups as they work while keeping an ear out for misconceptions that need to be cleared or questions that need to be answered.
The official "formative assessment moves" (actions teachers in a classroom can quickly take to gauge how students are doing without using actual tests or activities) are:
Priming: preparing the students in advance on what they will be doing. This can be short term ("today class, we are going to look at punctuation.") or long term ("for the next few weeks, we will be analyzing Shakespearean sonnets").
Probing: asking direct questions to the students that activates schema.
Posing: asking more thought-provoking questions that are designed to get students' minds in gear.
Pausing: giving students time to digest information before asking them to express their thoughts.
Bouncing: asking questions randomly and rapid-fire around the room, "bouncing" from one student to the next.
Tagging: like spray paint tagging. It's when you write down student ideas on the board. Studies have shown that, when documenting student thoughts in the board, it is necessary to write all of them down-- even the weird ones-- on order to demonstrate that the classroom is a safe place to express any opinions and ideas (this boosting participation as shy students unconsciously feel safe enough to talk), and also that the best way to document such thoughts is via Word Web rather than a list, as a list subconsciously implies a hierarchy of worth regarding the ideas.
Binning: tends to come at the end of a lesson. It is a review of the information learned that day, perpetration of what is to come, and is akin to sorting the new knowledge into "bins" for the students to access later.
Modern pedagogical theory holds that to be truly useful, formative assessments (the activities where students produce something, not the moves listed above), should not be heavily graded (a 100 point test is not formative), should be low stress for the student, should be timely (you can't redirect the day's lesson if you only assess at the end of the day), and the data gathered should direct or guide the educator's teaching. If half the class cannot answer a simple entrance ticket question, then you need to take a step back and clarify some things, or else you are paddling a sinking ship.
There is a strong movement in modern teaching that formative assessments should also be ones in which students receive feedback and opportunities to better their performance. Gone are the days of teachers handing out zeros like candy. (My assessments professor-- because assessment and feedback are such a big deal now that they make you take a class on it-- often recalls how one of his students was nearly turned down for a job, but won them over when he answers the question, "do you hand out zeros?" With, "no. I use a system of incompletes. Any student who is willing to resubmit work in a timely manner can improve.")
The current desire for teacher who are willing to work with students and not just hand out zeros is so strong that feedback and assessment are major components of the PACT. This is because for the past decade or so, schools have been "teaching to the test" in a backwards attempt at improving. A side effect of this was that students were going through the rigmarole of standardized testing while not actually achieving mastery (or sometimes, basic comprehension) in needed areas. These days, schools are gradually moving away from this mentality, and educators who take the time to assess and provide opportunity to improve are hot on the market-- especially considering the current nation-wide teacher shortage.