(Pretty detailed explanation here).
Raid Mode is the mini-game in RER. Basically, there are 21 stages, and 3 difficulties - Chasm, Trench and Abyss. You can choose three weapons to take with you, and each weapon can have Custom Parts attached to them, which is sort of like the upgrade system in RER, there are loads of different kinds of upgrades you can find (you find them in both Story Mode and Raid Mode).
You play through various areas that appear in story mode, but there are a set amount and types of enemies to kill. Sometimes you have to kill the enemies to progress, sometimes not and you can run past them. In addition, there are sometimes locked rooms that you can get keys for, for extra goodies. You have a start point, and you have to reach the finish point without dying.
Also, you have a level in Raid Mode. You start at level 1, and the maximum level is 50. It takes a while to get to level 50 so it gives you something to work towards. The enemies also have levels 1-50, so you can tell how tough an enemy is based on their level.
There are enemies that have icons next to their level sometimes too. A shield icon means that the enemy has a strong defence, so it takes a lot more bullets to kill it. One icon signifies speed - they are smaller than normal enemies, but much faster. Fist icons show that enemies have higher strength, so their hits are more damaging, and finally bosses have crown icons.
As you progress, getting higher levels, the weapons available to you will get stronger. Weapons have levels required to use them, so you can tell from the level, as well as the stats, if it's a good gun. The amount of Custom Parts you can add to a weapon varies, so that can be an influencing factor on whether or not to use a higher level weapon - a higher level weapon may have slightly higher firepower, but if you add a custom part to your old one, it can boost the firepower over. So there's a lot of tactical decisions to make.
The store in Raid Mode allows you to stock up on ammo, weapons etc between stages. Also available in the shop are ammo bags, which mean you can carry more ammo with you - the upgrades are staggered, starting with ammo bag 1, and finishing (I think) with ammo bag 5. You can do the same with grenades and herbs, getting holders for these too so you can take more with you, which is necessary for the more difficult stages.
Finally, there are lots of different kinds of missions that give you rewards for completing them. You can keep getting missions, sometimes they do repeat themselves, such as 'BOWs based on wolves. Defeat 20 of them'. The rewards from completing such missions are points to spend in the store, new characters and new outfits for these characters.There are ten characters to chose from, all of whom star in this game, and each has their own ability (for example, Chris has shotgun and rifle mastery, meaning he can reload these weapons 200% faster).
It sounds very complicated but it's really not. It's a very fun experience, you'll be playing it for hours.

It's so much fun playing both alone and with other people too, there's so much that's cool about this mode, and I think it makes a very nice change from mercenaries.

Sorry for the long explanation.
