A wedge is a tool used to split logs of wood. The thick end is hammered and
the thin end steadily widens the opening until the log falls apart. The
proverb means that a small beginning will lead, it is hoped (or more often
feared), to something greater.

> ‘The building of just one house isn’t going to spoil the beauty of this
stretch of countryside.’

> ‘But it’s only the thin end of the wedge. One house will be followed by
another, and before we know where we are there’ll be scores of them.’