The attachment of O and E (or of other letters) is called a typographic ligature. Ligatures were often used in ancient languages (such Latin and ancient Greek) to mark a diphthong or sometimes simply to make writing easier in pre-press times.

In modern French, the œ ligature is linguistic as opposed to aesthetic. It bears an important linguistic role, mainly because oe and œ are not pronounced the same. When you have an œ in your word, you will not pronounce the o and the e separately, like you would in coefficient, for example. As a rule of thumb, words of Latin origin will pronounce œ as /œ/ or /ø/ ¹ (for example œuf, sœur, œil, cœur) and words of Greek origin will pronounce it /e/ (like fœtus, Phœnix, Œdipe). There are also a few words that pronounce it as /ɛ/ (like œstrogène).

¹ This is IPA for French, if you don’t know it, there’s a nice chart on Wikipedia.

Essentially, the “oe” together tells you how that vowel is to be pronounced, as in the word “œuvre”. Think of it as an extra vowel that has it’s own distinct spoken sound (pronunciation). I remember learning this in elementary school. Hope that helps.