As a noun: 'some' or 'a few' — an unspecified small number or amount (common in formal/written contexts).
若干の修正が必要ですが、全体としては問題ありません。
Some corrections are necessary, but overall there is no problem.
若干の応募者が条件を満たさなかった。
A few applicants did not meet the requirements.
若干の在庫は倉庫に残っている。
There are a few items left in stock.
As an adverb: 'somewhat' or 'to a certain extent' — indicating a slight degree or amount.
この部屋は若干寒いので、上着を持ってきてください。
This room is somewhat cold, so please bring a jacket.
結果は若干良くなったが、まだ改善の余地がある。
The results have improved somewhat, but there's still room for improvement.
彼の説明は若干分かりにくかった。
His explanation was somewhat hard to understand.
An archaic/literary sense meaning 'many' or 'a great number' — largely obsolete in modern Japanese.
古文では『若干の民、慶びにあふる』のような表現が見られる（古語的用法）。
In classical texts you can see phrases like '若干の民、慶びにあふる' (an archaic usage meaning many people rejoice).