A single-core processor is a microprocessor with a single core on a chip, running a single thread at any one time. The term became common after the emergence of multi-core processors (which have several independent processors on a single chip) to distinguish non-multi-core designs. For example, Intel released a Core 2 Solo and Core 2 Duo, and one would refer to the former as the 'single-core' variant. Most microprocessors prior to the multi-core era are single-core. The class of many-core processors follows on from multi-core, in a progression showing increasing parallelism over time.
Processors remained single-core until it was impossible to achieve performance gains from the increased clock speed and transistor count allowed by Moore's law (there were diminishing returns to increasing the depth of a pipeline, increasing CPU cache sizes, or adding execution units).