The terminology can be somewhat confusing.
A Parliament exists between general elections. Under the Fixed-Term Parliaments Act 2011 the present UK parliament will exist until 2022. This is because the Act requires Parliaments to have a fixed term of 5 years but the Act also specifies when early general elections can take place. Had the recent Vote of No Confidence in Her Majesty's government been successful then it could have led to the Dissolution of Parliament and a general election - dissolution being the formal end of the Parliament.
A Parliament is divided into Sessions. A session is normally for one year. Following the 2017 General Election, the Government announced that the first session of this Parliament would last for two years to “give MPs enough time to fully consider the laws required to make Britain ready for Brexit.” This is only the second time since 1945 that Parliament has been asked to sit for a two-year session. The other was in 2010/12, following the formation of the Conservative-Liberal Democrat coalition government. That was the longest session in UK parliamentary history, lasting 295 days.
Prorogation - is the formal name given to the period between the end of a session of Parliament and the State Opening of Parliament that begins the next session - see Parliament - Prorogation
Parliament's website informs us that - "The Queen formally prorogues Parliament on the advice of the Privy Council" and that "Prorogation usually takes the form of an announcement, on behalf of the Queen, read in the House of Lords. As with the State Opening, it is made to both Houses and the Speaker of the House of Commons and MPs attend the Lords chamber to listen to the speech."
Prorogation brings to an end nearly all parliamentary business but Public Bills may be carried over from one session to the next, subject to agreement.
So, if Parliament were to be prorogued then any Bills proceeding through either House of Parliament would be stopped in their tracks - at least until Parliament reconvened in a new session. Several Bills considered essential for an orderly exit from the EU would not be enacted.
Prorogation therefore usually takes place as part of the routine operation of Parliament as it moves from one session to the next. BUT, prorogation has an interesting history and shows that prorogation has not always been a routine matter.
Tudor Monarchs frequently prorogued Parliament once they had used it to secure what they wanted !
Charles I prorogued Parliament in 1628 and in 1629. From March 1629 to April 1640 Charles I ruled without Parliament. The "Long Parliament" was summoned in 1640. The "Cavalier Parliament" lasted from May 1661 until January 1679 but had several prorogations, the last being when it was prorogued by Charles II in December 1678.
Much more recently, the Parliament elected in 1992 was prorogued in 1997 in advance of an embarrassing report by Sir George Downey into "Cash for Questions" and see The Telegraph 31 May 2013. Downey's report was issued in July 1997 after the General election won by Labour under Tony Blair.
Canada offers another example of prorogation being used for purely political reasons. In early December 2008, the situation for Stephen Harper’s second government appeared dire. Although he had won the election of October 14, Canadians gave his Conservatives only a minority government. Now, in the few short days since he had convened Parliament, he had so angered the opposition parties that it appeared they might combine forces and defeat his government in a vote in the House of Commons. While Harper would then have the option of requiring another election in an effort to win a renewed mandate from Canadians, the opposition was talking of forming a coalition government to replace the Conservatives. In order to avoid defeat, and the possible loss of power, Harper resorted to a somewhat novel instrument: he asked the Governor General to prorogue Parliament. The Governor General agreed to his request and issued a proclamation accordingly. The first session of Canada’s 40th Parliament ended only 13 days after it began. See the very interesting article by Charles Davison at Law Now - Prorogation: A powerful tool forged by history
Prorogation is therefore possible but, given that key government legislation could not be enacted in time for Brexit on 29 March, it would be a far from sensible strategy however convenient it may appear to some individual MPs. The nation would be left in an even more precarious position than it may already be in.
*** Prorogation 27 April 2017 ***
The time-honoured prorogation ceremony held on 27 April 2017 may be seen via Youtube. Royal Assent was also given to some 23 Acts of Parliament. The 2015-17 Parliament was dissolved on 3 May and the General Election 2017 held on 8 June - see Parliament 2015-17.
See also the Orders of the Privy Council meeting held on 25 April 2017
This BBC item from 2015 may also be of interest - La Reine le veult: What is prorogation in Parliament?