Bulgarian lands across the Danube

So you know how there is a big river called the Danube that flows through Europe? Well, on one side of the river is Bulgaria and on the other side is another country.

Now, back in the olden days, a long long time ago, Bulgaria used to have lands on the other side of the Danube too. But then some things happened, like wars and people moving around, and those lands were taken over by other countries.

So now, when people talk about "Bulgarian lands across the Danube," they are talking about those old lands that used to belong to Bulgaria but don't anymore. It's kind of like if you had a toy that you used to play with all the time, but then you gave it away to someone else, and now you still remember it and sometimes wish you still had it.