Update 17 July 2015
Relevant images from the Chief Inspector's glossary can now be referred to for the 'official' descriptions...
Some additional terms...
And because it's relevant here, the Chief Inspector's definition of 'entry clearance'...
As 'pnuts' suggested, ECO stands for Entry Clearance Officer. They are a mid-level Crown Servant employed by the Home Office but attached to the Foreign Office and posted to a British consulate abroad. They make decisions on Entry Clearance applications (see How Entry Clearance Decisions Are Made). They report to an ECM, Entry Clearance Manager.
Entry Clearance applications are their term for visa applications made abroad. Some situations require the person to have an entry clearance prior to arrival, hence the term 'entry clearance'. Not everyone requires an entry clearance, some nationalities, like Canadians, can arrive without one and get 'leave to enter' at a border control.
Because they are attached to the Foreign Office and posted abroad, an ECO generally has the diplomatic rank of Vice Consul. This convention is the same throughout the Commonwealth and the USA uses the same diplomatic conventions. ECM's have the diplomatic rank of Consul.
The counterpart to an ECO is the Immigration Officer (IO). They work in airports on British soil and issue 'leave to enter' (also known as 'visa on arrival') to those who do not require an entry clearance. (NOTE: see Visitors from the USA for a relevant article) They also examine and stamp entry clearances. The IO can cancel an entry clearance and place the holder in detention for removal. They can also detain and remove people asking for 'leave to enter'. Because of this and a few other factors (like standing and having to wear a uniform), IO's get paid more and have more opportunities when they leave the government.
NOTE: While there is ONE set of rules, the IO must refer to the Immigration Directorate Instructions whereas the ECO refers to the Entry Clearance Guidelines. Incredible numbers of people on the net mix these up and hence get it wrong. The IDI's and ECG's are NOT the rules and lots of mistakes get made by people treating them as if they are the rules.
NOTE: ECO's do not have to be British nationals, sometimes they will hire the spouse of a British national who has moved abroad. Sometimes they will make a local hire as an Entry Clearance Assistant (ECA) who rises up to become an ECO. Dedicated crown service is a way to acquire British nationality.
NOTE: As long as we're nitpicking on terminology, I can add that the British Embassy absolutely NEVER issues a visa. It's not their job, they don't know how, and they are not authorized, and if they tried they would get fired. Visas are issued by a consulate. The same holds true for the rest of the Commonwealth and other countries like the USA, Japan, etc. They may be in the same building, but they are not the same thing.
NOTE: I wrote both linked articles but have no connection to the site. And the site itself has no commercial content.