What are Gems and what is the Update Tick procedure trigger?

A gem is a dropped item/block (for example, when you drop an item with Q (by default)).

The tick rate event happens at every tick rate of a block. You can customize the tick rate, there is an option when making/editing the block. By default it's 20 (so it's exactly a second, because 1 second = 20 ticks). This is useful for making machines or crops.