The System Management Controller (SMC) is a subsystem of Intel processor-based Macintosh computers. It is similar in function to the older SMU or PMU or UAE of non-Intel Macintosh computers, as well as the newer T2 Security Chips made by Apple (more information here; spoiler alert, they're really annoying).
The SMC has roles in controlling thermal and power management, battery charging, video mode switching, sleep and wake, hibernation, and LED indicators. It also enables enforcement of the macOS End User License, allowing macOS to identify when it is running on non-Apple hardware.
To reset your SMC, see this page.
For older machines (Ivy Bridge Haswell and Broadwell), see this page.
For CD3215 without T2 chip, see this page.
For CD 3215/17 with T2 chip, see this page.
For a more in-depth explanation of how the SMC circuit works and basic functionality, see this page.
To reflow, solder and/or replace the SMC, see this page.
For more info on the SMC circuits, see this page.
For SMC sensor codes, see this page.