In general, a tool is an object that can be used to aid in accomplishing a task.
The alembic is optional and decreases the magnitude of all negative potion effects. So if you are planning on creating just positive effect potions, you will not necessarily need this apparatus.
The calcinator is optional and increases the magnitude and duration of ALL effects, both postive and negative.
Mortar & Pestle Edit
The retort is optional and increases the magnitude and duration of all positive potion effects.
A lockpick is used for picking the locks of doors and chests.
The Skeleton Key is an unbreakable lockpick which also increases Security by 40 points. Obtained as a reward from Nocturnal's Quest, for PC users the item ID is 0000000B.