Public domain works can be used by anyone without having to pay royalties as they belong essentially to everyone, i.e. the public. In the United States the current term of copyright is 75 years from the date of copyright. That term has changed at different points through the years as copyright law has been amended. Be aware that different countries like Canada and Germany have their own copyright laws and periods to abide by. Also be aware that just because a particular piece of music has fallen into the public domain that doesn't mean that a specific arrangement of a piece has also.
Arrangements have copyrights just as compositions do.
Besides the legal concerns, which can be fuzzy and hard to understand, there's the human impact of illegal copying. You're one of the hardest workers around here. Bill's, Joe's, and Tony's work to do too. Neither should you make and distribute illegal copies of sheet music or recordings. Violating their copyrights makes it that much less likely that they'll continue providing high-quality music for you.