Single-core
A single-core processor is a microprocessor with a single core on a chip, running and computing a single thread at any one time. The system of single-core consumes a considerable amount of time by doing so. A major improvement occurred after the emergence of multi-core processors which have several independent processors on a single chip and can perform many functions at a time.

Increasing parallel trend
 Single-core one processor on a die. Since about 2012, even most smartphone CPUs marketed are no longer single-core; Microcontrollers are still single-core, while there are exceptions.
 Multi-core a 'few' processors on a die, e.g. 2, 4, 8.
 Many-core a 'large number' of processors on a die, e.g. 10s, 100s, 1000s. Some specialist ASICs/Accelerators and GPUs fall into this category.

References

Computer architecture
Microprocessors
Flynn's taxonomy