What is the SI base unit of luminous intensity?

The candela, and it is the only SI base unit defined around human perception. The others measure the world; this one measures how bright something looks to us, weighted by a standard curve of the eye's sensitivity across colours.

That matters because the eye is far more sensitive to green than to deep red or violet. A green source and a red source emitting identical power do not have identical candela values, which is why exit signs and warning lights are chosen in the colours they are, and why the shift to green laser pointers made a modest power increase look dramatic.

The name is the old unit made rigorous: brightness was once expressed in candlepower, from an actual specified candle of stated wax and burn rate, then from a platinum surface at its freezing point, and since 1979 from a fixed value for a monochromatic green source. One candela is still roughly one candle. The related units follow from it - the lumen is candela spread over solid angle, the lux is lumens landing on a square metre.