What is needed to certify an aerodrome as an airport in Canada? So here.
All airports are aerodromes. All aerodromes are not airports.
Difference between Airport and Aerodrome:

An aerodrome or airdrome is any place from where flight operations can take place. This can include an airstrip in the middle of nowhere to a commercial airport in the biggest city in the world. An airport is a special type of aerodrome that has satisfied certain certification criteria or regulatory requirements of the ICAO that a regular aerodrome may not have achieved.
The term airport implies a certain stature of having satisfied certain certification criteria or regulatory requirements of the ICAO that a regular aerodrome may not have achieved. Hence it can be said that all airports are aerodromes, but not all aerodromes are airports.

So then what facilities and services does an aerodrome need to have, in order to be certified as an airport in Canada?
Original Answer
Aerodrome
It is an area where:

aircraft land
aircraft take off

Runway may not be present (in case of a water aerodrome).
Airport1
By definition2, an airport is an aerodrome with facilities for commercial aviation flights to take off and land
It is an aerodrome which has:

facilities to store and maintain aircraft
at least one designated operational landing/takeoff area (runway or helipad)
hangars
terminals
fixed base operators
airport aprons
air traffic control centers
passenger facilities (restaurants and lounges etc.)
emergency services
customs3
immigration3

Edit
I noticed that the question is updated to be only for Canada. In that case, airport requires the following:


have a safety management system in place
comply with airport safety standards and security requirements


Further reading
Aerodrome
Airport
Airport Design and Engineering Standards (by FAA)
Aerodrome Standards (PDF by ICAO)

1: Not all airports must have all of these to qualify as an airport.
2: I could not find specific regulations which define an airport.
3: In case of an international airport