Short version:
Federal transfer payments are basically meant to help provinces and territories provide services to their people.
There are many types of transfers, the 3 main ones being:
Canada Health Transfer
Canada Social Transfer
Equalization and Territorial Formula Financing
and the others being:
Federal Trust Funds
Nova Scotia Offshore Arrangements
Newfoundland and Labrador Offshore Arrangements
Quebec Abatement for federal programs that Quebec has replaced with its own programs and for which it obtains a compensation.
Health
The largest transfer from Ottawa to the provinces, it provides predictable funding for health care and protects the principle of universality of health care in Canada. (If a province wants this transfer, it has to have universal health care). Paid on a per-capita basis.
Social
Social transfer support post-secondary education, social assistance, social services and early childhood development. Paid on a per-capita basis.
Equalization
Serves to help less prosperous province provide public services that are reasonably comparable to those in the other provinces.
Equalization entitlements are determined by measuring provinces' ability to raise revenues. This means how much can a province generate in revenues from taxing its residents. The bigger the salaries of the residents, the higher the "capacity of the provincial government to generate tax revenues is", the less equalization it gets.
Equalization has nothing to do with provincial expenditure or debt or the services that it provides.
Why don't the have not provinces become "have" provinces?
The short answer is that salaries are lower in have-not provinces or unemployment is higher.
The longer answer must reflect the mix of industries in each province. As Ontario has a large banking and financial sector which provides a large amount of well paying jobs, the Atlantic provinces rely more on the fisheries, tourism, agriculture and hospitality sectors which generate low paying jobs.
Quebec is the highest taxed province in Canada and despite this, its government has a hard time generating per-capita revenues that are equal to the Canadian average.
If Quebec was to lower its income taxes to the same level as Alberta, Quebec would get even MORE in equalization payments than it gets now. If Quebec was to abolish its sales tax like Alberta, Quebec would then get more in equalization from Ottawa.
It is not the amount that is spent by a provincial government that counts, it is the capacity of that government to raise revenues that determines the amount of equalization it will get.
Territories
Territorial Formula Financing is an annual unconditional transfer from the Government of Canada to the three territorial governments to enable them to provide their residents a range of public services comparable to those offered by provincial governments, at comparable levels of taxation.