What does the United States' 'Separation of powers' entail?

The US's separation of powers refers to the complete separation between the three branches of federal government; the legislature (Congress), the judiciary (The Supreme Court) and the executive (The Presidency). This system was born out of a resentment by the founding fathers of the tyrannical power demonstrated by British monarchs, and rests on the principle of 'checks and balances'. That is, each branch can have its power 'checked' and limited by the other. For example, a President can be impeached and removed from office by Congress, whilst the President has the power to veto Congressional bills, (of which can be overidden by a two-thirds Congressional majority). 

This stands in direct contrast with the UK system where branches are fused together. The executive (the Prime Minister & Cabinet) and the legislature (the UK parliament) are merged together and, in theory, acts as one body of power when the Prime Minister's political party holds a parliamentary majority.

The judiciary also used to be fused into the UK parliament with the presence of Law Lords in the House of Lords, who represented the highest court of appeal in the UK. However, this was replaced by an independent Supreme Court in 2009. 

Ultimately, the US's separation of powers is a hallmark of US democracy and one of the main differences between the UK/US system.