In order to mine a block, miners must provide Proof-of-Work in the form of a valid hash of the block they intend to publish. A hash is essentially a large number, and for a hash to be valid, it must be smaller than a defined target, which is set by Bitcoin’s ruleset. The difficulty of publishing a block is then a precise inverse of the target.
This difficulty is dynamic: it updates every 2016 blocks—roughly 2 weeks—to ensure Bitcoin blocks come in roughly every 10 minutes. If more miners join the network and mine blocks at a faster rate, difficulty will rise. If miners stop mining, and blocks arrive slower than every 10 minutes, difficulty will fall.
In a technical sense, the Bitcoin network sets the target rather than the difficulty. All valid Proofs-of-Work must be below this target. The difficulty then, is simply the inverse of the target. If the target is raised, this makes it easier for miners to find a hash below the target, so the difficulty has been lowered. If the target is lowered, the difficulty has been raised.