Definition: A microbend is pretty much what it sounds like: a tiny, little bend of a joint. Even calling it a bend is a bit of an exaggeration; it's actually a softening of the joint. Microbends are so subtle, it won't really look like you are bending your knee, but you will feel a difference in the pose as the muscles around the joint kick in to provide support. Microbending is recommended for standing yoga poses where there is a tendency to lock the knee, like triangle pose. Locking the elbow joints can also be a problem in poses where the body's weight is supported by the arms, like upward facing dog, so a microbend of the elbows would be appropriate here.
Why Microbend?: Microbending protects your joints from unnecessary wear and tear. Take a pose like triangle. While you are trying to get the front leg super straight, if you lock the knee into its fullest extension, you are actually stressing that joint. Microbending is especially important for people who hyperextend, taking their joints past straight. By microbending, we allow the skeleton to come into better alignment while engaging the muscles surrounding the joint instead of relying on the joint itself. This is essential for the development of long term joint health. It may feel funny at first and you will definitely notice your muscles working differently, but it will soon become second nature and is a good practice to engage in, even if your teacher doesn't mention it every time.