High performance computing (HPC) is computing done on a large cluster of servers to reduce the time needed to perform a large computational or analytical task. This approach uses parallel processing, which involves several computers breaking down individual tasks to work together simultaneously to complete the task more efficiently than is possible on a single computer. Cloud computing has made high performance computing more accessible because it has reduced the cost of purchasing and/or managing multiple servers.
The U.S. Geological Survey provides an overview of high performance computing that includes typical computational barriers and relevant quotes from scientists: https://www.usgs.gov/advanced-research-computing/what-high-performance-computing.
This Google video provides an animation explaining high performance computing: https://www.youtube.com/watch?v=nIBu1EFYmBU.