Nicehash is a Bitcoin cloud mining service and Multipool. Nicehash allows you to rent mining gear which is hosted by the users of Nicehash who are mining on the Multipool. When someone is mining with their own gear using Nicehash, they are mining on the Multipool. If someone rents their rig, they rent the rig for a set PPS rate which is paid to the miner and Nicehash also takes a cut.
Nicehash also runs the Blockchain Lottery, where you can set up solo mining orders for Bitcoin, Litecoin, or DASH. The cost of this can vary, but the more you rent the better your chances. If you solve a block, you get 99% of the found block, and Nicehash takes 1% as a fee. This is better than solo mining on your own node, as the Nicehash nodes have a lower latency than you could manage on your own connection, ensuring your block is broadcast and not orphaned (lost, due to someone else getting the same block out before you).
As a miner, you can earn more than regular pools, and you can point your GPU, CPU, or any ASIC (X11, SHA256 OR Scrypt) and get paid PPS for each. It will select the most profitable coin for your hardware and algorithm chosen and they have a mining calculator to help you with this, although payout is always in Bitcoin. Using the Nicehash service pays you directly in BTC no matter what you mine, and you can earn much more Bitcoin using a GPU using Nicehash than a regular pool, as it can use the GPU for any other algorithm that it is not SHA256 or Scrypt. You could use it for these also, but its electricity wasted! The calculator is shown below:
You can use your Nicehash account to store coins but do not mine coins directly to your Nicehash address, and storing large sums in any online wallet is not recommended! Nicehash can be a fun way to play the Blockchain lottery by renting a large farm for a short time, although cloud mining to mine in pools and not solo for profit can be difficult, but if you wait you can sometimes rent hash low enough to do this. They are best used for their Multipool with your mining gear and their pay rate is higher than most other pools.