Executive order

An executive order is any legal decree by the President of the United States that is effectively law, but can be overwritten by either Congress, the Supreme Court, or any succeeding presidential administration. Presidents however are limited as to what they can decree, as it must be in accordance with federal law, and is therefore subject to judicial review. A big problem with executive orders is that they can be overturned by succeeding administrations, as is seen by Trump's purging of anything even remotely related to Barack Obama.

Legality
The President's power to create and enforce executive orders are based off of Article II of the United States Constitution, which gives the POTUS wide authority to determine how laws are enforced and to what degree they are enforced. They also derive from Acts of Congress that delegate to the President some degree of lawmaking power, called "Acts of Delegation". It should be stressed, as it was above, that this doesn't give the President carte blanche power to rule by decree, and the executive orders of the President are limited in scope and are subject to judicial review.

Abuse
That said, executive orders are still ripe for abuse, such as Executive Order 9066, which was the executive order that enabled Japanese American internment during World War II. Given the time it was given, it is perhaps unsurprising that the courts ruled in favor of the legality of this otherwise blatantly unconstitutional order in the Supreme Court case Korematsu v United States (1944). However, this decision was overruled in Trump v. Hawaii (2018).