Not sure if my input is going over what people already know, but below is my take on how DPFs work. I'll try not to run on.
To meet ever stringent emissions VMs (vehicle manufacturers) have after treatment systems to help. This means that engine out emissions are trapped and dealt with in the exhaust. The 2 main systems are DPF and SCR. Diesel Particulate Filters trap particulates on a filter bed, whilst Selective Catalytic Reduction uses a catalytic reaction (chemical type reaction) to convert NOx into less harmful gases (essentially into exhaust gases that aren't harmful and arn't legislated for). SCRs need an additional fluid to generate the reaction called urea, which is now sold in liquid form on petrol station forecourts as adblue. New cars like the Merc blue efficiency etc have SCRs and need to periodically fill up with adblue to keep the SCR happy, but anyhow back to DPFs.
A DPF has to periodically clean the filter. It does this by burning off the particulates when the ECU detects that the filter is full, this process is called regeneration. Regeneration can occur in two ways, passively or actively. PASSIVE regen is when the exhaust gases out of the engine are hot enough to cause the DPF to burn off the stored particulates, and conversely the other type of regen is ACTIVE whereby something additional has to happen to raise the exhaust temp high enough to burn off the particulates on the filters.
The something else tends to come from burning additional fuel sometime before the filter in one of 2 main ways.
In cylinder post injection is the first method, whereby additional diesel is injected through the existing fuel injectors into the combustion chamber very late in the combustion cycle (i.e. when the piston is close to BDC, bottom dead centre). When it burns, the energy is not converted into energy to turn the wheels but into heat energy in the exhaust gases. This raises the combustion gas temperature and hence the engine exhaust gases sufficiently to burn off the filter.
The second method is called HCI or Hydrocarbon injection. This is where diesel is injected into the exhaust via an additional fuel injector in the exhaust. When this burns it raises temperature in the exhaust and again causes the DPF to regenerate.
VMs would use either post Injection or HCI to regenerate, and both methods have drawbacks. It would appear that Honda have used post injection. The main problems with post injection are around effectiveness, service life and drivability, which I'll try to explain below, but it's worth mentioning these problems are more for Honda design engineers to sort out rather than things we should all worry about.
When you squirt fuel into the cylinder late (as a post injection) you risk squirting fuel onto the cylinder walls and the you get an increase in fuel found in your oil and hence reduced service intervals and specialist oils (so if Honda recommend an oil quality, I'd stick to it)
The other issue is that with in cylinder post injection whilst most of the post fuel burned is turned into heat, a bit of it is turned into energy to push on the piston and hence turn the wheels. The problem with this is that when the system regenerates the driver would notice a torque step which would feel like a small surge which is not desirable. Engines are generally calibrated so that this effect is combatted by a reduction in the main fuel quantity so no surge is felt.
So why is intervention required? When DPF is full and it not passively or actively regenerated (I.e. You haven't driven hard enough to passively regenerate, or the post injection isn't capable of increasing temperature to regen) then a light or massage appears on the dashboard to tell the driver that he needs to do something before it becomes critical. Now i'm not familiar with how the 8th gen system works on the Accord, but there are two ways this could happen. Either a preset programme (if Honda designed one) will cause the DPF to regen stationary at theside of the road, or the driver will need to take their car to dealer and they will plug in their service tool and will force a regen in the workshop.
So my advice to drivers of DPF equipped cars ... Give it a good thrashing every once in a while .... Like anyone needs an excuse ;-)