While the exact origin is unknown, "everything but the kitchen sink" is said to have been used somewhere during the early part of the 20th century, and later made popular during World War II.
"Everything but the kitchen sink" is the notion that it's possible that if people had to evacuate their homes on short notice, or if they were moving to another location, they would want to bring all of their belongings with them. Some things though, like kitchen sinks, were heavy, connected to various pipes, and bolted down.
Obviously, taking something like that along isn't very convenient, so it's left behind while everything else is taken. Even refrigerators, ovens, microwaves, washing machines, dryers, and air conditioners could be unplugged and taken. So they took all of their belongings with them, except the kitchen sink. The kitchen sink was left behind not because it wasn't wanted but because it just couldn't be taken.
Some people also relate this expression to robbers who steal everything they could from a house. If someone says, "He took everything but the kitchen sink" you can best believe that the robbers took a lot of things. They would have taken the kitchen sink if they could have easily disassembled it and carried it.
The earliest time that this phrase was used was on "Queen for a Day," an American radio and television show in 1945, where viewers could win huge prizes. There was a woman who won many prizes, and the host said she's "won everything but the kitchen sink!"
The next time you hear this expression, think about this article and smile because now you know what it means.