The recent Garlicoin hard fork uses a new mining algorithm. The large jump in difficulty is due to miners having a higher hash rate with the new algorithm.
All minable cryptocurrencies have a target rate that blocks should be mined at. Since coins are created when blocks are mined, this is the rate that coins enter circulation. For Garlicoin the target block rate is 40 seconds and the mining reward is 50 GRLC. So, we can expect that 50 new Garlicoin enter ciruclation every 40 seconds on average.
Miners create blocks by solving a cryptographic puzzle using the computing power from their CPU or GPU(s). The 'network hash rate' is the total number of computations happening per second. In order to keep a consistent block timing, the difficulty adjustment algorithm changes the difficulty of the puzzle to keep the rate that blocks are mined at consistent. If the hashing power doubles, then we expect the difficulty to double as well.
For more information on how blockchains and mining works, I highly recommend watching these videos created by Anders Brownworth: Anders Blockchain Demo.
Garlicoin can be mined using the CPU/GPU in any computer.
To get started mining Garlicoin see the official Garlicoin resource website: Garlic Recipes by Pandawan.