Break the ice
To break down social formality and stiffness.
The earlier meaning of this phrase, i.e. 'to forge a path for others to follow' alludes of course to the breaking of ice to allow the navigation of boats. The figurative use is quite old and was recorded by Sir Thomas North in his 1579 translation of Plutarch's Lives of the noble Grecians and Romanes:
"To be the first to break the Ice of the Enterprize."
It wasn't until the latter part of the 17th century that it took on its current 'establish a relaxed relationship in socially awkward situations' meaning; for example, Samuel Butler's Hudibras, 1678:
"The Oratour - At last broke silence, and the Ice."
If we move forward another two hundred years 'breaking the ice' reverts to its original usage, when specialist ice-breaking ships were introduced. These ships, known as ice-breakers, were equipped with strengthened hulls and powerful engines, were employed in the exploration of polar regions.
Soon after the ships were introduced the term 'ice-breaker' began to be applied to social initiatives which were intended to get strangers acquainted with one another. In 1883, Mark Twain used the wordb that way in Life on Mississippi:
"They closed up the inundation with a few words - having used it, evidently, as a mere ice-breaker and acquaintanceship-breeder - then they dropped into business."