In the U.S. the branches as a whole are balanced, a single part of the legislative branch has limited abilities to directly affect other branches. The only unilateral thing they can do with any impact is issue subpoenas to compel attendance to committee meetings. The House of Representatives does have a couple other useful abilities that ultimately require the Senate to agree. The House is the originator of appropriation bills and files articles of impeachment. Impeachment and removal is unlikely with a hostile senate and it's an action that is just as likely to cause political backlash for Democrats as help them. Appropriation bills are commonly used as a game of chicken for shutting down some or all of the government, but such brinkmanship is almost universally disliked by the population at large and success in previous shut down has been mixed for both parties.
Controlling one part of the legislative branch does allow for more effective opposition to things requiring congressional approval, in the current Trump Presidency the big things that require approval would be constructing a border wall, further tax cuts, and immigration reform. A divided congress will generally only cause things to slow down even more, full control of a branch of government is generally needed for either party to implement their own policies with any success.
