While mining for resources & crafting stuff are the main drives of the game... there's also adventure & exploration elements, as you'll venture into the unknown. You'll discover various biomes in addition to generated structures (like desert & jungle temples, wooded & swamp mansions, underwater shrines, abandoned mineshafts & underground strongholds).
Minecraft tends to encourage emergent gameplay, where you effectively make your own fun. Some things I've seen are...
* Defeat the Ender Dragon -- This is typically consider the end-game boss of Minecraft, which most people go fo.
* MCHC100 -- You try to obtain all the achievements in-game on HARDCORE MODE, typically offline. In this challenge, the game world dies with you (the game deletes it in the process. For online worlds, you're either banned from the world OR gets permanently placed in Adventure Mode (where you can explore the world, but you cannot actively interact with it).
* Punch-a-chunk / Chunk-out / Punch-Chunk Challenge -- This is an interesting challenge where you mine out every single block (with the only exception of bedrock) out of a single "chunk" (a unit of the game world) with a few restrictions & rules (like you're not permitted to mine any blocks outside your chunk, you have to made do the blocks your chunk provides, ect.). It's generally more interesting in a competitive environment (like a head-to-head challenge), but it still challenging on it's own.
* Play a challenge mod or world -- Two example of this are SuperHostile Worlds & SkyBlock Modded worlds. SuperHostile Worlds, as the name suggests, are worlds that are geared to have a lot of mob generators throughout the world as you struggle to obtain colored blocks of wool to each preset objective. SkyBlock modded worlds start with one single block in the "sky" (with nothing but void below you) & you have to complete objectives in order to obtain new blocks & survive in this somewhat extreme world.
You may find these interesting OR come up with something that you enjoy challenging yourself with. You can do whatever you want within Minecraft, so the limits are ultimately what you want to impose upon yourself.