An item of minor importance dominating a situation.
This expression probably originated in the USA. There isn't a specific incident that it refers to that can be located there but there are many instances of it in print in US publications from the 1870s onwards, whereas there are none that come from any other country until well into the 20th century.
The earliest citation that I can find is from The Daily Republican, April 1872:
"Calling to mind Lord Dundreary's conundrum, the Baltimore American thinks that for the Cincinnati Convention to control the Democratic party would be the tail wagging the dog."
Dundreary is a character of Tom Taylor's play Our American Cousin. He was an amiable but dim nobleman, who frequently coined nonsensical riddles and twisted metaphors. These 'Dundrearyisms' were similar to Malapropisms and were briefly in vogue amongst US theatre-going circles in the 1850s. For example, 'a stitch in time never boils', 'better late than sorry'.
That Dundreary association leads nicely on to a witticism made by S. J. Perelman, the US humorist. He twisted the phrase after reporting his escape from the attentions of a group of prostitutes - 'It was a case of the tail dogging the wag'.