A mining rig is a computer built with the purpose of mining cryptocurrency. Hashrate is how powerful a mining rig or device is.
When Bitcoin was released, mining was just a hobbyist affair with your everyday computers joining in on mining whenever work wasn’t being done. Back then mining was done on the processor or CPU (Central Processing Unit) of a computer,
Eventually miners moved on to more efficient and powerful GPUs ( Graphics Processing Unit) which were able to provide magnitudes greater mining capability than a CPU. It should be noted that both CPU and GPU mining make use of hardware available to the consumer and easily purchasable on your local computer store or online.
Since then mining for cryptocurrency has meant more and more specialized hardware to provide the best efficiency and hashrate, this can be seen in Bitcoin mining where professional miners congregate in areas with cheap electricity and use specialized hardware called ASIC (Application Specific Integrated Circuit) whose only purpose is to compute for Bitcoin’s Proof of Work. One downside of this move towards specialized hardware is the centralization of mining power in several mining pools and mining corporations.
Methods to prevent centralization of mining power are being implemented in newer blockchains like Ethereum and Monero to provide true decentralization of mining power.