Origins
Ivan the Terrible was not a bad ruler. He was a terrifying one. The word terrible originally meant 'inspiring terror', from Latin terribilis, from terrēre — 'to frighten, to fill with dread'.
For centuries, terrible carried genuine power. The terrible swift sword in the Battle Hymn of the Republic is awe-inspiring, not poorly made. A terrible beauty, in Yeats's phrase, is one that frightens. The word described things that made you tremble.
The weakening began in the 17th century. Terrible food. Terrible weather. Terrible traffic. The terror drained away, leaving only a general sense of 'very bad'. This process — strong words losing their force through overuse — is one of the most common patterns in language.
Later History
Terrific followed the same path but in the opposite direction. It too meant 'causing terror' (a terrific storm was a frightening one), but it drifted upward into enthusiasm. By the 20th century, terrific meant 'wonderful'. Two words from the same root, one falling, one rising.
The Latin terrēre produced a tight family: terror, terrify, deter (to frighten away from), and terrorist (one who uses fear as a weapon). All preserve what terrible has largely lost — the genuine sense of dread.