What does “coming apart at the seams” mean?

Question

Meanwhile, Europe’s single currency is coming apart at the seams.

In the example above and in general.

Answer 1

It's an idiom. Referring to clothing.

It means that something is falling apart, or declining in quality, as clothing would if it were torn at the seams.

Seam: A line where two pieces of fabric are sewn together in a garment or other article.

Answer 2

bursting (or bulging) at the seams informal (of a place or building) full to overflowing.
come (or fall) apart at the seams informal (of a person or system) be in a very poor condition and near to collapse : the attitude of the airport guard was symptomatic of a system falling apart at the seams.

^NOAD
An earlier version of this second expression was give way at the seams, seen in print in its literal sense from the mid 19th century. The first figurative use of the phrase I could find was from Across the Campus: A Story of College Life by Caroline Fuller, 1899:

The related phrase bursting at the seams came first, but all versions of the phrase seem to have followed similar paths in their trek from literal to predominantly figurative use: