Wikpedia puts it nicely:

"The concept of concurrent computing is frequently confused with the related but distinct concept of parallel computing,[3][4] although both can be described as "multiple processes executing during the same period of time". In parallel computing, execution occurs at the same physical instant: for example, on separate processors of a multi-processor machine, with the goal of speeding up computations—parallel computing is impossible on a (one-core) single processor, as only one computation can occur at any instant (during any single clock cycle).[a] By contrast, concurrent computing consists of process lifetimes overlapping, but execution does not happen at the same instant. "