The Patient Protection and Affordable Care Act (aka "Obamacare") includes an "employer mandate." Large employers, defined as having at least 50 full-time employees (or 50 FTEs), must provide health insurance for their full-time employees or else pay a penalty. The mandate was supposed to begin on January 1, 2014.
However, the Obama administration decided to delay implementation of the mandate until 2015. Even in 2015, the administration will only enforce the mandate for employers with more than 100 employees who fail to cover at least 70% of their full-time employees. Further still, even in 2016, the administration will only enforce the mandate for employers who fail to cover 95% of their full-time employees.
The House's argument is pretty simple: The president can't re-write the law to change dates, and which employers are covered, and how many employees the employer needs to insure. That's a pretty clear legislative function.
President Obama (more specifically, the executive officers and departments named in the Complaint) has not filed an answer yet. Presumably he will argue some type of executive discretion to phase in the legislation and some discretion to target only the most egregious offenders in the law's early implementation.
Frankly, I don't know enough about this area of the law to assess how strong of an argument that will be. Also, there will be some question of whether the House has standing to even file such a lawsuit. I should note that part of the lawsuit challenges public funding of programs for which Congress has not allocated funds. It will definitely be interesting to see how this plays out.
This is not directly on point, but if you missed SNL's I'm just a bill/executive order skit then you should definitely check it out.