A Canadian Controlled Private Corporation (CCPC) is a company within Canada who's majority of voting shareholders (51%) are owned by Canadian Residents who are either Canadian Citizens or hold permanent residency (PR). A company cannot be classed as a CCPC if less than 51% of the controlling vote is held by non-Canadian residents. There can be limitations to this as even if you are a Canadian Citizen or have PR status, your status is based on your taxation residency and other ties to Canada (Family/Dependents) which could impact or later change the status of a CCPC.
Example of CCPC Status:
A major shareholder in your company is a Canadian Citizen, but decides to move away to another country for an extended period of time, it is possible that the company may lose it's status of being a CCPC. In this case you will be seen in the eyes of the law/CRA as a non-resident and any voting shares in the company will reflect this.
The above eligibility for a CCPC also applies if a company is held by subsidiaries or other means by which the company's controlling vote is not held by a Canadian resident.
If you are buying real estate in Canada using a "Holdco/OpCo" setup, there are some advantages to having a CCPC, the main being certain small business tax rates, eligibility for Lifetime Capital Gains Exemption (LCGE) and more general advantageous taxation rules.