The expanding earth theory is the idea that the earth was significantly smaller 200 million years ago, and at that time the land continents as we know them made up 100% of the earth's crust, and were also mostly covered by water. Then over time, the earth's surface expanded and split along the modern day fault lines, creating large rifts in the crust, and allowing the mantle exposed by this process to cool and become ocean floor. Meanwhile, the water on top of the original crust drained away to the new ocean crust, making the older crust dry land.
I believe this theory makes more intuitive sense and is better supported by evidence than the current geological model of continental drift propelled by oceanic spreading.
I don't think the lack of a known mechanism behind the phenomenon disproves the theory. There are other theories accepted in modern day thought (like the Big Bang Theory) that lack a known mechanism.
(The mechanism is atmospheric release. The Earth decompressed from "gas giant" phases of evolution after it was finished forming in the interior of the star.)