What is this quadruple triangle logic symbol?
As Nick states, it is a transmission gate. Think of a TG as a switch that can connect or disconnect the horizontal line. 

As Ignacio states, in this particular case the TG is used to disconnect the external pin from the digital input synchronizer when the chip is in SLEEP mode. Note that at the same time that input is grounded by activating the FET. 



Note that the signal that is passed to the synchronizer is digital , so in normal operation a TG would not be needed. The only reason I can think of to use a TG (instead of a simple gate) is that in sleep mode the value on Pxn might not be a valid digital signal, which would cause excessive switching and hence current consumption of the schmitt-trigger and subsequent circuitry.

The standard implementation of a transmission gate is two FETs in parallel, one P and one N. The two FETs require opposite switching signals.