To self-assess means to calculate how much HST should be paid on the purchase of a good or service when the supplier has not billed HST or just billed the Federal Component (GST) of HST on an invoice.
The self-assessment rules apply to all purchases by the University. Despite the general rules discussed in the link below (updated in Oct-19), the University will almost never require self-assessment on purchases made within Canada. The exception is where a foreign organization, which is not registered for HST, performs a service within Canada.
Taxable goods and services delivered and/or performed in Ontario should be charged HST unless the goods and services qualify for exemptions, point of sale rebates, or are zero-rated supplies.
It is the responsibility of the individual/department initiating the purchase to determine if goods or service needs to be self-assessed for HST.
For a high-level, scenario by scenario assessment please take a look at the GTFM Policy.