I hear this quite often when referring to 22lr rimfire ammo.
Meh .. so you clean your gun after 500 rounds instead of 600 rounds.
I shoot a lot, and won't pay double the price for a 5% cleaner round.
My opinion ....

To me "dirty ammo" is when it leaves large amounts burnt and sometimes unburned powder in the action and barrel. Also "dirty ammo" tends to be very smoky. In my experience dirty ammo usually equals cheap, off brand and Western European. If you want to compare to "clean ammo" try some loads made with Winchester 296 powder. After shooting over 100 of my own reloads in .44 mag through a new Ruger 77/44 rifle, I went to do a quick clean and wipe down and found absolutely ZERO fouling or powder residue in the barrel ....nothing. Buy good quality ammo from brands you know and stay away from the cheap stuff or military surplus from outside the U.S. Shoot more and be safe.

Many surplus ammo vendors buy military surplus ammo. As they have to buy in bulk lots, they have to take the good with the bad.
As a result they may get lots that the brass is discolored, grungy, or somewhat corroded. Due to the age and condition there may be no fires, hang fires, etc in a certain percentage of the ammo. They sometimes will attempt to "polish/tumble" the ammo to clean it up.
If the vendor is reputable he will advise of the potential of possible misfires. This ammo should be fired with caution and especially
not in semi-autos. This is especially true with the military Mauser ammo as the 8x57 mm. I know this for a fact as a friend of mine
worked at an Miami surplus dealer where this was done.
Some people link "dirty ammo" to non-corrosive but that is not really true a I have fired good military surplus with corrosive primers which do require immediate cleaning> NOTE virtually all the US ammo in WWII was corrosive except for the M1Carbine.

It can be somewhat subjective, however, Aaron A summed it up nicely for you in one sentence. You also will be able to tell the difference when you clean your weapon after it has been shot. "DIrty" ammo will be noticeable upon cleaning, compared to other shooting sessions with higher quality ammo.

It mainly refers to carbon residue left over from firing the weapon, usually the result of cheaper powders or low quality

The worst case meaning of "dirty" ammo would be cartridges utilizing corrosive primers, at least with respect to modern loads. This used to be common, but is thankfully rare nowadays. Most commonly encountered with old military surplus ammo, eg. 30 or 40 year old European made 8x57 Mauser. If you think your ammo is corrosive, make sure to CORRECTLY deal with the salts left behind in the barrel and chamber or you will have a rusty problem on your hands.

I believe this is very subjective. I have also read reviews say dirty ammo and I do not see much difference.

As a handloader for 35 years I have come across powders that are clean burning or those that leaves a residue or byproduct of the combustion process. This is a problem more more semi automatic firearms as the action becomes built up quicker with leftover residuals eventually causing a malfunction of the moving parts. Bottom line.. clean burning ammo ( powder) allows you to shoot longer at a single siting with less chance of malfunction due to built up sludge which starts to cook and solidify. Obviously you should clean at the end of your session regardless.