What this suffix does
-fold comes from Old English "-feald" (fold, layer) and forms adjectives and adverbs meaning "multiplied by X".
twofold = double (multiplied by two).
threefold = triple (multiplied by three).
tenfold = ten times as great.
hundredfold = a hundred times as great.
manifold = multiple, of many layers (many + fold).
In a sentence: "a tenfold increase" = an increase to ten times the original.
Manifold: the most literary and philosophical
"manifold" = multiform, varied, of many kinds. From "many + fold" (many layers).
In philosophy: the "manifold of experience" (Kant) = the raw data of experience before it is organised by the mind.
In engineering: a "manifold" = a pipe fitting that connects several outlets from one inlet.
In literary prose: "manifold difficulties" = multiple and varied difficulties. "the manifold forms of injustice." C2, very formal.
Journalistic use of -fold
In economic and scientific journalism, -fold is extremely frequent:
"a tenfold increase in cases" = cases multiplied by ten.
"profits rose fourfold" = profits quadrupled.
"a hundredfold improvement" = an improvement of a hundred times.
It is more precise and more formal than "ten times more" or "quadrupled." Appears constantly in The Economist, Financial Times, Nature, Science.
Note: "increase tenfold" = multiply by ten (the final total is ten times the original). Do not confuse with "increase by ten" (adding ten to the original).