At the moment it’s not clear whether space mining is legal. Although there’s nothing expressly forbidding asteroid mining by private companies, the Outer Space Treaty declares that no nation can own property in space. The wording of the treaty is vague enough that companies want to ensure they’ll own the resources they mine from asteroids before investing millions or billions of dollars trying to extract them.
The bill would make those property rights official, at least under U.S. law. Although companies can’t own the asteroids themselves, the current version reads:
http://www.popsci.com/congress-votes-to-legalize-asteroid-mining