ものを is a grammar point that functions in a similar way to のに in that it will express that (A) is something that was desired, despite (B) being the actual result. However, it is primarily used when the speaker is trying to convey their displeasure at the result of (B), due to (A) being something that by all means should have happened.
ものを will be translated as 'if only (A)', or '(A), but (B)'. Despite being a construction of もの and the adverbial particle を, ものを is often considered as a standalone conjunction particle. It can be seen following verbs or い-Adjectives in their standard form, or な-Adjectives followed by な.

• もっと早（はや）くに歯医者（はいしゃ）に行（い）けば歯（は）を抜（ぬ）かずに住（す）んだものを...
  If you went to the dentist earlier, they wouldn't have had to remove your tooth, but…
• 目（め）を合（あ）わせなかったら止（と）められなかったものを、なんで警察（けいさつ）なんかと目（め）を合（あ）わせちゃうんだ。
  If you didn't make eye contact with the police, we wouldn't have been stopped, so why did you have to go and make eye contact with them?
• アレルギーなどがあったなら、さきに言（い）ってくれればいいものを...
  If you had an allergy, you should have let me know beforehand, but…
• 「手伝（てつだ）って」って言（い）えばいいものを、一人（ひとり）でやるからこう言（い）う目（め）に会（あ）うんだよ。
  If you have just asked for help, but because you did it alone, it ended up like this.
• みんなでやれば簡単（かんたん）なものを...
  It would have been easy if we all worked on it together, but…
• 道具（どうぐ）を使（つか）えば楽（らく）なものを、わざわざ自分（じぶん）の力（ちから）でやろうとするから怪我（けが）をするんだよ。
  It would have been easier if you used tools, but because you went out of your wat to try it without any tools, you ended up getting hurt.

As can be seen in the above examples, ものを is almost always preceded by hypothetical structures such as ば at some point leading up to its use.