I use Western Union money orders all the time; it's easier than an out of the way trip to the post office for me.

Anyway, that space is for you to sign, not the person you're giving the money order to. If you don't sign it, the other person may send it back and ask you to sign it, then mail it to them again. They may just sign it themselves, but a lot of people will send it back to you.

You should definitely sign it, especially on a money order for such a large amount. If you don't and the person tries to cheat you later, you may want to file for a refund on the money order from Western Union. That will be easier if you have signed this space, because they will be able to see that you purchased the money order if it was cashed.

There is also a long line for an address labeled Purchaser's Address, or something very similar, beside it. That is for your address.