From TouchDesigner 088 Wiki

Storage refers to storage of python data in a running TouchDesigner process. Storage is a standard python dictionary associated with any operator. Values stored in this dictionary are persistent, and saved with the operator. The storage dictionary contents may be manipulated directly with methods such as OP.fetch() or described below, or examined with an Examine DAT.

It is stored with, value) and retrieved with n.fetch(key, default)

Automatic Cooking

When an element of storage changes, expressions that depend on it will automatically cook.

Preserving in Files

Storage is saved with .toe and .tox files and loaded on startup.

See Storage in OP_Class.