What: Finding your position on the Earth as if you were going around the Equator (i.e. east to west), known as your Longitude. Finding your latitude, where you are between the poles is simple. This is done by measuring the angle of the Sun at midday and has been calculated accurately for centuries. Longitude on the other hand is far more difficult.
Before John Harrison, Dead Reckoning was used to find your location. Essentially this maps out where you are based on where you were, how fast you have been travelling at and the direction you were travelling. Imagine that you are doing this at Sea, the current could easily alter your course without you even knowing it, you are suddenly hundreds of miles from where you should be.
An Act of Parliament in 1714 established the Longitude Prize for which there were several categories of prize money depending on the accuracy of the solution. Several people attempted to produce a solution, however, it was John Harrison who realised that time pieces, clocks and watches, were the key. He set about creating ever more accurate devices.
What If: The Longitude problem had not been solved?
The British Navy lost ground to other countries that had either solved the Longitude problem or had somehow developed better navigation methods. The British Empire would have declined and possibly Napoleon succeeded in invading Britain. Even if he did not, the British Common Wealth would have ceased to exist. America would not have claimed its independence as fewer ships arrived from Britain or successfully arrived in America, indeed the slave trade would have been much smaller. Australia would also have had fewer ships from Britain arriving. America and Australia could even have been invaded or colonised by other countries, possible France.
In summary, Britain would not have formed its second coming of the Empire or Commonwealth and may even have been invaded by France.