The blue jelly, j, is a NetHack monster. It is famous for being completely immobile (although there are other monsters with this characteristic), and is often summoned for precisely this property for use with e.g. boulder forts, stashes, etc. They cannot attack directly, but it is still possible to die from their passive attack, which causes you to be "suddenly very cold", especially with inexperienced players. This monster is blind (you can "see" this effect by polymorphing into one). This monster is considered vegan for eating purposes.
If you attack a blue jelly without killing it, and you do not have cold resistance, it will gain HP equal to half the damage it inflicts on you. Attacking it, even if you miss, may cause the blue jelly to divide in two (“The blue jelly multiplies from your heat!”).
Avoid attacking in melee unless you have cold resistance, as blue jellies are much tougher than might be expected. At their base level, they do (4+1)d6 damage, which gives a range of 5-30, and they can be generated at much higher levels. Ranged attacks are preferable, but make sure you have enough ranged weapons to finish the job as you won't be able to retrieve that lovely stack of daggers until the jelly is dead.
If you lack cold resistance and have sufficient HP, you may also be able to farm blue jellies for food or its two intrinsics, though you're likely to spend more nutrition splitting a jelly than you will get from the corpse.