A Visa (TRV) which is fixed on a passport is just an authorization to travel towards canada. it can be single entry or valid for several years. multiple entry visa or TRV means that the holder of such a visa can travel towards canada multiple times as long it is valid.
When ever someone travels towards canada, at the port of entry he presents his/her passport having the visa. at this stage the CBSA officer allow/grant him an entry which is usually for 6 months and it gives the visa holder a visitor status in canada.
So once a person enter into canada he/she gets a visitor status (the immigration stamp on passport) and the Visitor status is usually valid for 6 months which means the person can only stay in canada legally for 6 months (no matter his visa is valid for several years still he is only allowed to stay in canada for 6 months). In simple words multiple visa means one can make multiple trips to canada and each trip/stay can only be of 6 months.
Now if the person wants to stay more than 6 months (his allowed time to stay in canada) due to any reasons.. he/she can do this by submitting an application for an extension to stay in canada. anyone living in canada for more than 6 months without authorization will be considered illegal or overstaying in canada. To get this authorization to stay more is called "extension to stay/remain in canada as a visitor".
Extension to stay:
extension to stay applications can be submitted online or through paper (online applications are faster). in case of parents, children, spouses, inland/outland sponsorship, awaiting PR, willing to get married, to spend more time with family members etc are rarely refused. the application of extension is made atleast 30 days before the expiry of the visitor status of a person. if your visitor status/visa/allowed time expires you cannot file an extension application. so you must be with a valid status to make such application. if status is expired then you have to apply for "restoration of status"
On approval the person gets a visitor record ( a document mailed to his home address) which is valid for the requested time or usually for the next 6 months. when someone leaves canada his visitor status or visitor record expires.
Example:
Mr xyz had a 10 years multiple visa on his passport. he entered into canada on 1st January 2013 so legally he is only allowed to stay in canada till 1st of july (i.e only 6 months). on 25 june he submitted an application to extend his stay in canada for another 6 months for the reason that he wanted to spend more time with his family, CIC approves him and he is allowed to stay in canada till 1st jan 2014.
again during his stay his wife sponsored him and now MR xyz is awaiting his PR status so on 20 December 2013 (before 1st jan 2014) he made another application to extend his stay in canada again for the reason that he wanted to stay more with his wife and he is awaiting PR decision. cic again approves his stay and now this time CIC grants him 1 year extension means he can live in canada with a legal status till 1st jan 2015.
NOTE: no matter mr xyz visa was valid for 10 years but still he needs to extend his stay in canada as he only allowed to stay in canada for 6 months. Even if Mr xyz had single entry visa instead of multiple visa still the same rule apply.
Important: if you make an extension to stay application too early it may be refused so it should be made near to the expiry of current status BUT before expiry as one can only apply for extension with a valid legal status.
How to apply for extension:
go through this link http://www.cic.gc.ca/english/visit/extend/visa.asp
if you want to apply online: http://www.cic.gc.ca/ctc-vac/getting-started.asp
a) check your eligibility
b) create a mycic account
c) fill/upload your application forms
d) pay your fee
e) submit your application
hope it helps you understand how extension to stay application works
