Why would your phone's GPS fail without Einstein?

Your phone's GPS would fail without Einstein because the clocks on GPS satellites don't keep the same time as clocks on the ground. Speed slows them down and weaker gravity speeds them up, exactly as relativity predicts, and together they leave each satellite clock about 38.6 microseconds a day ahead. Left uncorrected, your position would drift by roughly 11.4 kilometres every day.

Why do a few millionths of a second matter so much? GPS works by timing. Each satellite broadcasts its position and the time, and your phone measures how long the signals took to arrive. Radio waves travel at the speed of light, so each delay tells you a distance, and with at least four satellites in view the receiver can work out where it is. At that speed, tiny timing errors become big distance errors.

Two effects pull in opposite directions. The satellites circle about 20,200 kilometres up, fast enough that special relativity slows their clocks by about 7.2 microseconds a day. But up there Earth's gravity is weaker, and general relativity makes their clocks run faster by about 45.8 microseconds a day. Gravity wins.

Not everyone believed it at first. During GPS's early development, some thought general relativity would not affect it, until an experiment in which atomic clocks were flown around the world on airliners showed that it would. So engineers set each satellite's clock to tick slightly slow before launch, at 10.22999999543 MHz instead of 10.23 MHz, and once in orbit it keeps pace with clocks on Earth. Every time your map finds you, Einstein is quietly being taken into account.