Hypothetical concessive adverb: 'even if it were the case that...'. Often used with ~ても or ~たとしても to emphasize that the outcome would be the same regardless of the condition.
もし is a simple 'if', while よしんば adds the nuance of 'even if' or 'granting that'.
Etymology
The exact derivation is uncertain; it may be a contraction of an older concessive expression. The kanji 縦 is used for its meaning of 'even if' or 'supposing', but the word is now almost always written in kana.