English-Canadian is a loose term that generally refers to the non-francophone, English-speaking majority population of Canada.
Traditionally, it has referred to anglophone Canadians, that is to say Canadians who are of British descent. In this case, the term refers to language, not ethnicity; perhaps the majority of Canadians of British descent are Scottish or Irish, not English.
However, with this population ever-shrinking as a proportion of the whole, the term is now often applied in a much broader sense, referring to all Canadians outside of Quebec, including English-speaking immigrants.
Striking a balance between "French" and "English" has been a political issue in Canada for quite some time. In the cabinet of the Prime Minister of Canada, for example it is often expected that he will have some degree of balance between the amount of "French" and "English" cabinet ministers. Likewise, the office of the Governor General of Canada is said to alternate between "French" and "English" persons.