The capacitor across the isolation barrier returns capacitive displacement currents that are generated by the high voltage swing of the primary winding.  Without this capacitor or other techniques (like shield windings to reduce the generation of these currents) the currents flow via the distributed capacitance to earth ground back to the input and are measured as conducted EMI.

As the cap bridge the isolation barrier they must be safety rated hence the Y rating.  See AN-15 for more info.  There is a maximum value (2.2 nF) to limit the line frequency current that also flows through the Y cap - again this is covered in AN15.

Cheers

 Crusher

Thank you.

Took this snapshot from AN-15. How does the Y CAP connection as highlighted in RED offer a lower impedance path from Node B (Earth closer to secondary side) to Node A (Earth near Input Terminals)? 

The main source for EMI in a typical SMPS is the switching voltage across the transformer primary, consisting of the switching frequency and its harmonics, as well as the high frequency content of the switching transitions. This voltage  is distributed across the width of the primary, and is coupled to the secondary via stray capacitance, which is also distributed across the width of the winding.

I took a fairly typical SMPS transformer and measured the interwinding capacitance between the primary and secondary using an impedance bridge, and it was on the order of  ~25 pF.  So, you have a distributed high frequency voltage source coupled to the secondary side of the supply via a small distributed capacitance - a current source, as it were. If this current source is allowed to operate unimpeded, it will pump high frequency displacement current out of the output  terminals of the power supply, where it can picked up by an EMI receiver and register as interference. 

The primary - secondary Y1 capacitor essentially shorts across the EMI current generator with  a capacitance value much larger than the typical transformer interwinding capacitance. It can be effective either when hooked between the primary return, or alternatively can be connected between secondary return and primary B+, depending on the results from EMI testing. This Y1 primary-secondary capacitor is one of the most important elements in abating EMI. If it is accidentally removed, this generally results in a drastic increase in mid-band EMI, sometimes as much as 10 dB above the quasi-peak limit - an EMI mountain, as it were.