The Break is a reference to the period following the 1996 outbreak of The Flu in Dimension Two on the Starz Original Series Counterpart.
During the decade before "The Break", the timelines of Dimension One and Dimension Two were mostly synchronous, with world events closely duplicated in both.
In 1986, during the Cold War between the United States and the USSR, there was an accident during an experiment in the USSR-controlled area of East Berlin. At the time, the universe split into two identical copies (Dimension One and Dimension Two).
The worlds were identical at the moment The Crossing opened. While some slight differences are noted within the first decade after the duplication, world events followed mostly along the same track until The Flu outbreak in Dimension Two reached its peak in the mid-1990s.
EDITOR’S NOTE: This HD timeline image from Love the Lie offers some specific details of divergence between the dimensions. Along the top, from left to right, recognizable images include an original Tamgotchi, the collapse of the Berlin Wall, Nelson Mandela, an original Walkman, the crew of the doomed Space Shuttle Colombia, a close up of cigarette butts, an original iPod, a 50 Euro note, former Libyan dictator Muammar Gaddafi, deceased North Korean Dictator Kim Jong Il, a sounder of swine, smoke rising from the twin towers, an original iPhone, singer Prince, and a county-by-county results map of the 2016 US election.
Along the bottom timeline you can see the Space Shuttle Challenger explosion, leaders Mikhail Gorbachev and Erich Honecker of the old USSR, an erupting volcano, what appears to be a closeup of an Ebola virus, a mosquito on someone’s arm, pedestrians in surgical masks, and a giant sea turtle.
The Dimension Two timeline diverged significantly with the death of 7% of D2's human population during the first four years of the flu's spread. The political and cultural upheaval that followed the pandemic caused Dimension Two to focus their scientific efforts on health and safety with tremendous developments in the medical field such as treatments for HIV and mapping the human genome (both developments were then shared with D1).
D2 Europe outlawed tobacco products and made it a crime NOT to report illness in yourself or your neighbors. There is also some indication that the pork industry, at least in Europe, is no more. There is a cultural taboo against eating pork because the disease spread from swine to human.
Dimension One, completely unaffected by the disease, seems to have carried on very much like the "real world" with consumer-driven developments in personal computing and electronics and little specific focus on large-scale scientific exploration to bolster the common health and welfare.
Creator Justin Marks tells Counterpart Starz Wiki that this point of great divergence will be further explored in the series.