Thanks, bro. 
Ok, now that we know what each physically is, what's the governmental relationships and realm of authorities between them all? 
Westminster is the primary legislature of the United Kingdom, with certain local issues being devolved to a Parliament in Scotland and an Assembly in Wales. N. Ireland has an assembly but years of unrest since the Good Friday agreement has led to its suspension.
Local councils have authority to implement local policy, but cannot do things such as create new crimes or in any way pass legally binding acts outwith their remit: I.E. Part of Glasgow City Council can decide what speed limits to put on a road in Glasgow, or another part can decide where to spend the most money on trash collection; They cannot however set those speed limits above the nationally legislated limit of 70MPH, nor can they decide to terminate all domestic trash collection on a whim.
The House of Commons (UK Parliament) and I believe Local councils are elected using the First Past The Post system, whereas the Scottish Parliament (and I believe the welsh assembly) are elected using Proportional Representation (it is argued that this has allowed a lot of smaller parties to gain a voice in the parliament, but there is dispute as to its true representation of the electorate).
The Scottish Parliament does not "answer" to Westminster in the truest meaning of the word, but depending on who is in power at any one time the First Minister (Scotland) will often defer to the will of the Prime Minister (UK) if they are political allies or of the same party. Several issues are reserved for action at Westminster only, such as defence.
Finally, there is an unelected body called the House of Lords, which is based on inherited and granted titles (Peerages). This body has the final say on all legislation passed by Westminter Parliament.* While from the outset having an unelected body decide the final fate of bills passed by an elected one may seem dangerous and undemocratic there have been occasions where they have proven their worth: A recent example is their opposition to National Identity Card systems; While a shameful compromise was eventually agreed, the Lords had at least slowed the process down. Additionally, they prevented a British version of the Patriot Act (including the right to hold suspects without trial for over 30 days - the antithesis of British justice!) from passing - some, myself included, are grateful for that. The Magna Carta has a lot to answer for, eh?
*In principle the Queen must also ratify all legislation to be presented before Parliament at the start of each legislative year, but in practise she would never be allowed to publicly oppose the duly elected government.