Since Aoi's guide is geared more towards the mechanics of the tube for acquiring nodules and the slimeling I figured I'd try to make more of a newb intro and basic mechanics guide to go along with it. Here goes.
The basic mechanics are very simple. There are 1000 slimes to kill. Raising ML (monster level) counts towards additional kills. Different tiers of ML will change the slimes you encounter, affect the items you get, and the number of turns of coated in slime you get. The fewer turns of coated in slime you have the more slime damage you'll take.
0-100 ML slimes will drop slimy sweetbreads, slimy fermented bile bladder, tiny slimy cyst, wad of slimy rags
gives 10-11 turns of Coated in Slime
101-300 ML slimes will drop tiny slimy cyst, slimy sweetbreads, slimy fermented bile bladder
gives 9-8 turns of Coated in Slime
301-600 ML slimes will drop small slimy cyst, slimy sweetbreads, slimy fermented bile bladder
gives 7-5 turns of Coated in Slime
601-1000 ML slimes will drop medium slimy cyst, slimy sweetbreads, slimy fermented bile bladder
gives 4-2 turns of Coated in Slime
1000+ ML slimes will drop big slimy cyst, slimy fermented bile bladder, slimy sweetbreads
gives 1 turn of Coated in Slime
If your goal is farming marbles for the trophy then 301-600 ML is optimal. Medium and big slimy cysts both drop unique non-tradeable items so if you want those items you either have to gather them yourself or buy them in the mall. If you're trying to gain stats those items can be sold to help pay for chamoix (if you need them). Currently the ML increase from slime hates it gear (created with nodules and slime covered items) is better than anything else. Stat gains greater than clover or sign gym adventuring are possible which is very useful for leveling up quickly.
If your goal is lowest possible turn count (slimeling perhaps) you have to change gear, MCD (mind control device, detuned radio, or The Annoy-o-Tron 5000) and familiar to lower ML to get higher turns of coated in slime since lower turns (high ML) will instantly kill you. You also have to CLEESH or escape combat with divine champagne popper (or similar) items to avoid killing the slime with lower ML. That pretty much requires using KoLmafia and the script mentioned later in this tread since doing all that manually every few adventures is too time consuming. The slime suit has excellent elemental resistance so collecting that is very useful for trips to Fernwarthy's Basement or other cases where elemental resistance is needed. Some of the items crafted with nodules are quite useful. The prismatic damage and MP restore of the malevolent medallion for example. Hopefully this partially answers the question of what is the point of the slime tube.
The wiki has most of this information so some of this is redundant.