While battling through your lessons, you will notice that each stage drops a specific set of gems and bonus items. All stages are guaranteed to drop at least 1 Gem — with the number of gems dependent on RNG (random number generator) — as well as some amount of Grimm.
How much Grimm you'll receive per battle will depend on your battle score as well as what lesson the stage is in. The higher in number the lesson, the more Grimm you'll earn. Hard Mode stages will drop more Grimm than those in Normal Mode.
Bonus drop items like Watches, Mugs, etc. are not guaranteed and also based on RNG. The majority of battles will only drop a single bonus item, but some stages have the potential of dropping items x2. These are listed in the last table below.