Most often, feng shui corner is another way of saying feng shui bagua area. This expression is often used in the BTB, or Western School of feng shui to nominate different bagua areas.
So, yes, in this context the feng shui corners are very important as you need to balance each and every bagua area for good feng shui in your house.
They are not actually corners, just areas in your home as defined by the bagua, or the feng shui energy map.
Another way the words feng shui corner are used is to define the importance of corners as feng shui areas that attract and store large amounts of energy; usually low, negative energy.
This is the reason why in feng shui space clearing sessions it is always recommended to focus on house corners and clearing the stagnant energy there.
Because of this pulling effect, it is also recommended for good feng shui to have in your corners: