There are many social skills they learn while playing board games such as taking turns, interacting with other children and adults, communicating verbally and of course sharing.
They learn number and shape recognition, grouping and counting. Many games they learn letter recognition which will lead to reading skills. While working with the game pieces they are working on their eye-hand coordination and manual dexterity.
While spending this time with you, they are expanding their attention span, their ability to focus and how to follow rules.
So take out those board games and have some fun while your child learns!