To stonewall is to deliberately hold something up or delay it, especially by refusing to cooperate or answer questions. A big company might stonewall when its workers try to negotiate for higher pay — and your parents might stonewall when you try to negotiate for a higher allowance.
A press secretary stonewalls when she avoids directly answering a reporter's pointed questions, and you stonewall when you change the subject rather than commit to visiting your grandma. The word stonewall was coined as a nickname for Confederate General Thomas J. Jackson, who was described as "standing like a stone wall" as the enemy approached. It was originally a noun, meaning "an act of obstruction."