Many; several; plenty (used adverbially or to modify a noun).
彼はいくつも資格を持っている。
He holds many qualifications.
いくつも店を回ってやっと気に入る服が見つかった。
I went to many stores and finally found clothes I liked.
いくつも理由があってその計画は延期された。
There were many reasons, and the plan was postponed.
In negative sentences, it often means 'not many' or 'not much' (as in 'not many X').
その問題は答えがいくつもあるわけではない。
That problem doesn't have many answers.
彼女にはいくつも友達がいるわけではないが、信頼できる人が何人かいる。
She doesn't have many friends, but there are a few she can trust.