Well, there’s power on paper and power in real life.
On paper, the Senate is almost the equal of the Commons - about the only difference is that money bills must originate in the Commons. But both Houses must consent to all bills, including money bills. It has a suspensive power in relation to some constitutional amendments.
However, in practice, the Senate lacks much power, because the Senators are all appointed by the Governor General, on the advice of the federal Cabinet. They hold office until age 75. As a purely appointed body, they lack the political legitimacy to exercise their powers in opposition to the elected House of Commons. By constitutional convention, the Prime Minister and the Government are responsible solely to the Commons. (Although there have been two Prime Ministers who sat in the Senate.)
This means that the Senate tends to be a house of detail; it may propose amendments to a bill to try to improve it, but rarely will oppose the bill in its entirety.
Of course, there are the occasional episodes where the Senate actually uses its powers in a significant way. The last time was in 1991, when the federal Government was proposing an abortion bill to replace the provisions struck down by the Supreme Court in R. v. Morgentaler. The bill passed the Commons, but failed in the Senate on a tie vote (the Speaker in the Senate can vote like any other Senator and does not have a casting vote; in the case of a tie, the motion fails). So as a result of that vote in the Senate, Canada is one of the few countries that does not have any regulation of abortion, other than the same sorts of professional guidelines that apply to other medical procedures.
What Cat Whisperer is referring to is the practice in Alberta to hold provincial “elections” to the Senate. They have no binding effect, simply a political exercise to put pressure on the federal government to appoint individuals who have been approved by the electorate.