Barack Obama used executive discretion in ways that previous presidents had not. For example, he created a visa program that allowed undocumented immigrants to live and work in the United States. He did so without supporting legislation from Congress.
Note that this exceeds the normal definition of prosecutorial discretion. Not only did he not deport these people, but he actually gave them a quasi-legal status. Yet there is no law that says that the president can simply provide legal status to immigrants without following the normal procedures.
Obama signed an international treaty without getting ratification from the Senate.
Obama appointed people to the National Labor Relations Board (NLRB) without Senate approval. While this was ultimately reversed, they were making decisions for some months first.
There is also an argument that Congress has delegated too much legislative power to the executive branch. For example, the aforementioned NLRB has certain regulatory powers. Some have argued that regulations are themselves legislation and should be passed by Congress. A similar argument ended the line item veto in 1998.
There's some confusion in the comments about executive orders. Focusing on executive orders is misleading. First, Obama has often substituted presidential memoranda for executive orders. From USA Today:
President Obama has issued a form of executive action known as the presidential memorandum more often than any other president in history — using it to take unilateral action even as he has signed fewer executive orders.
More importantly, most executive orders do not violate the constitution in any way. For example, Obama's second executive order simply created a requirement applied during the hiring process for political appointees. It only affected government employees, not everyday citizens. Focusing on raw numbers of executive orders, presidential memoranda, or whatever is the wrong approach.
Note for example that DACA (Deferred Action for Childhood Arrivals), the visa program from the first paragraph, was not started by an executive order nor even a presidential memorandum. It was initiated by a memorandum issued by Secretary of Homeland Security Janet Napolitano (not Obama). It has a fee, a form, and offers something like legal status. All without empowering legislation.
DACA may eventually be torn down by the courts, but that's a slow process. We're now in the third year and it's still being appealed.
