sometimes in kana as おかげで. Literally 'in the shadow of (...)', denoting that something is thanks to something else. It can also be used sarcastically (e.g. thanks obama)
部屋が汚いお陰で、どこになにがあるか全く分からない。 Thanks to my room being so dirty, I don't know where anything is (sarcastic).
友達が有名なおかげで、どんな高級レストランでも予約なしで入れる。 Thanks to my friend being famous, we can go to any fancy restaurant without a reservation.
ラーソンのお陰で、不自由のない生活が出来ている。 Thanks to Lawson, a life without inconvenience is possible.
At start of sentence
When placed at start of sentence, it functions the same but the thing it attaches to is the overall context. It essentially just becomes "thankfully, (...)"
おかげで、テストに合格することができました。 Thankfully, I was able to pass my test.
お陰で、いい休暇を過ごせました。 Fortunately, I was able to enjoy a nice holiday.