Here, let me strip away a bit of superfluous information, and also show a physical reality that doesn't come through on the schematic normally:
If the output isn't grounded (they used an earth symbol throughout this schematic, but I don't think it was intended to mean chassis ground), then the capacitance between windings drives switching noise between mains and output. A double whammy. Well, the load is usually enclosed in a metal box too, so maybe it doesn't go far that way, but the part sent up the mains wiring is important. And if it is grounded, then that output-side noise is shorted out, putting the full magnitude onto the mains side.
And what is a capacitor? Two metal plates with some space between 'em, right? A transformer has, well they're not plates, but wires, but they still cover a lot of facing area -- they have capacitance alright! So the source of interference as inter-winding capacitance is a major one. Also capacitance from switching node to heatsink to chassis, via transistor tab, is a notable one -- maybe not so much in these units, where the heatsink is usually a board component, but it's also hit and miss whether the heatsink is grounded (say to primary DC +/-, or the center tap between them), which is a prime way to deal with that capacitance, shunting its current to ground through a local loop rather than allowing it to couple onto the chassis. (The capacitance from heatsink to chassis is fairly small, 10s of pF I would guess, but still, that's more than nothing.)
So, the transformer has some ~100s pF between windings, and assuming the output is grounded, a line-to-ground capacitor in exactly the location shown, will help to shunt the noise from inter-winding capacitance, back towards its source. A common mode choke then increases the impedance, and another cap (usually) serves to filter it some more. Sometimes the latter isn't required; the CMC working against mains impedance might be enough by itself. It depends.
We can reduce the circuit even further, to an equivalent something like this:
Note that the mains wiring is modeled as two 50 ohm resistors to ground. This is a convenient fiction, compared to the real world where it could be anything (transmission line and antenna effects galore!), but it's also not far from this on average. (That is, the impedance may have peaks well above or below this magnitude, but it still centers around about this figure.) C1, L1 and C2 form the usual CLC mains filter; note that L1 has leakage inductance which acts to provide differential-mode filtering with C1 and C2. The leakage is much smaller than the total value, so much larger capacitors are needed (typically 0.047 to 1uF). R2 represents the AC load of the converter circuit itself. V1 and C3 represent the inverter (RF) source, and any offending coupling like inter-winding or heatsink capacitance. C7 is another, more direct option for 'Y' capacitance, shunting across the source directly (primary to secondary). Note that C3/C7 represent the isolation barrier. Finally, the secondary may have its own 'Y' cap to earth if it's intended to float, otherwise when hard-grounded we can take it as ground as well.
All three positions of 'Y' capacitor are shown: C4, the mains-inlet cap, not used on the above ATX supply; C5 is equivalent to the ATX's C2+C3 (note that C2 in the above diagram makes the lines act in parallel for RF purposes, so using a pair of 'Y' caps is somewhat redundant; either way can be used, though without an 'X' (line-to-line) cap at the FWB, they didn't have that option). And finally, since the output is ultimately earthed, we recognize the secondary-grounded condition, so C6 is N/A, and C7 is equivalent to C5.
Also, note that R2 effectively produces RF as well, hence the need for differential mode (line-to-line) filtering. This is smaller anyway -- it's shunted by big huge (electrolytic) caps for one -- so we don't usually mind that L1 is somewhat improvised as far as its DM filtering value. (Or perhaps not. Evidently they needed quite a bit more in the ATX supply, hence adding 'T' in series with the leakage (on the other side of the FWB; for RF purposes, the diodes are always conducting so we can ignore them), and an extra stage of DM-only filtering between C1-T1-C4. Perhaps their electrolytics had unusually high ESR. Which, compared to modern formulations, eh, yeah they probably did.)
Tim