When a transmission line is 1/4 wavelength long, it is essentially 90 degrees long to the signal - meaning that the signal goes through 90 degrees of its 360 degree cycle. When the line is shorted, this causes a -1 reflection (the signal is inverted and reflects back towards the input). A -1 reflection is the same as a 180 degree phase shift. Therefore, if you launch a signal into the line, it travels 90 degrees to the short, the short induces another 180 degree shift, then the reflection travels back another 90 degrees to the input. Thus, the total round trip is 360 degrees. This means that the signal coming back as a reflection is exactly the same as the injected signal, so no current flows (in theory), which is the definition of high impedance.