What does long-run level mean for exchange rate I am reading a paper by the economist Dornbusch. It says that exchange rate will converge to its long-run level. The rate appreciate if prices are initially below their long-run level, and, conversely, if prices are initially exceed their long-run level.

Now what does long-run level mean?
The long-run in economics is a technical term. It means, roughly "without any short-run constraints". What are short-run constraints? Well they're fixed costs like any contracts you've signed (like, say, your lease, your employment contract) and any capital that you've accrued or lack would be short-run constraints.

To give an illustrative example, a barbershop may want to increase profits and considers potential options. In the short-run he can increase the prices of haircuts or decrease his hours of operation. In the long-run he can move to another location where he'll have more room for additional chairs and such.

For currency exchanges, I'd imagine fixed costs would include trade contracts and debt. At any rate hopefully this answers your question.

edit: and "level" in this context just means the exchange rate itself. Since it is numeric, it can be said to have a level. You could change the word 'level' for 'rate' and it'd be the same meaning.