The way I think about it is this:
The trade balance is the major part of the current account. If we are running a trade deficit, so X-M <0 then we have more money flowing out of the country from the current account than is coming and we have a current account deficit.
The relationship between the following accounts in the long run has to balance:
Current account = Capital account + Financial account
Everyone always says balance with this relationship, but this is confusing as it isn’t balance in an accounting sense of the word. The idea is that the aggregate inflows and outflows of money have to be equal, so think of it as if we have a negative on one side of the equation we need to have an equal and offsetting positive on the other side of the equation.
Current account deficit (a negative) must be offset by a capital + financial account aggregate surplus (+)
If we assume the capital account as zero, we can see that the current account deficit must be offset by a financial account surplus. A financial account surplus happens when more money is coming into a country from the purchase of financial securities (among other factors) than is flowing out, so:
If we need a financial account surplus, other people must be buying our bonds, specifically the citizens of other countries. The citizens of these other countries are buying our bonds with their savings. So the statement in your post is true, our current account deficit as a result of a trade deficit is being financed in part or in whole by a surplus in our financial account, which is a result of citizens of other countries buying our debt securities (among other things). When they buy our debt securities they are building up financial claims against the domestic economy that have to be repaid at some point.
Sorry that was long, but I hope it helped.