What it communicates: Diamonds are forever, duh.
Unless you have Diddy money, the fact that you're willing to spend a few thousand dollars on this woman says that, at the very least, you doubt she'll be single and pawning your necklace off in some shady corner of Atlantic City next month.
A financial investment this large, particularly if you haven't made similar gestures in the past, also signals a deeper emotional investment, which she may view as a serious step towards marriage.
It could also mean that you've recently fucked up, and are hoping to buy win her affections back. A big ole' sparkly won't fix every situation, but (real talk) it will fix most.