A clog is a blockage, or something that gets in the way. A clog in your kitchen sink might mean you have to call a plumber before you can wash your dishes.
A clog obstructs water from flowing through pipes, and it can also be figurative, like a clog in your city's restaurant inspection system that makes it impossible for people to open new cafes. When clog is a verb, it means to cause such a hindrance. A completely different kind of clog is a heavy, wooden-soled shoe. In the 14th century, a clogge was a "lump of wood," and the verb first meant, "hinder with a block of wood."