Minis were introduced so that a trader with a few thousand dollars could write a covered-call against 10 shares of a very expensive stock. The options-multiplier is 10, so every quoted dollar of premium is worth $10 rather than $100.
In practice most mini series died from lack of volume, and the market solved the same problem with fractional shares and cheap ETFs. You still meet the multiplier idea whenever you trade an adjusted-option or a non-standard deliverable.
Example: a stock at $900. A standard covered call needs $90,000 of shares. A mini needs $9,000. Selling a $2.00 mini call collects $20, not $200 — an easy and expensive thing to misread on a confirmation.
Related: options-multiplier, deliverable, covered-call