To be precise, it's not actually parallel processing. The effects loop in the amp allows you to place effects in between the preamp and the poweramp of a guitar amplifier.
Lets start from the top:
In a typical guitar "amp", there actually exists
1. A preamp
2. A poweramp
3. A speaker
We call this a combo.
The preamp shapes your signal and is often overdriven, especially in the heavy 80's preamp distortion tones. The preamplifier provides voltage gain but no significant current gain
This signal is then sent to the poweramp, which does the heavy lifting, creating a strong enough signal to drive a speaker, which is essentially a magnet with wires. A poweramp can also be overdriven if pushed to it's limits, giving a more open, less fizzy AC/DC type of tone. More often, the poweramp is actually very clean with a much higher headroom as compared to the preamp. Most of the time amp distortion comes from the preamp section. Especially bedroom amps. The power amplifier provides the higher current necessary to drive loudspeakers.
Often we find 1 and 2 put together, which we call a head.
And the speaker seperately, which we call a speaker cabinet.
Sometimes you may find seperate preamps. Less common among guitarists. David gilmore famously used an ampeg preamp for many of his early recordings and tours.
So your typical chain when you plug straight into your typical amp is actually like this:
Guitar->preamp->poweramp->speaker
When we put effects "in front" of our amp, we have:
Guitar->effects->preamp->poweramp->speaker
What the effects loop does is give you a connection after the preamp and before the poweramp. Allowing you to do this:
Guitar->preamp->effects->poweramp->speaker
Why?
Because many guitarists rely on their preamp for their overdriven/distortion tones. If they want their delays to work on the overdrive tones, and not have the delays be overdriven instead, they would want to put their delays AFTER the preamp.
So what about the POD XT and similar effects?
These effects actually do the job of a preamp. They shape your signal in a way a preamp does, and gets it ready for the next stage: the poweramp.
Parallel processing?
Nope. There is nothing running in parallel.
preamp->stuff you put->poweramp->speaker. It's in series.