An investment account registered with the Canadian government that receives special tax treatment — such as tax-free growth, tax-deductible contributions, or both — in exchange for following specific rules around contribution limits and, in some cases, withdrawal conditions.
It's the umbrella term for accounts like the TFSA, RRSP, and FHSA — each with its own rules, but all sharing one thing: the government gives up some tax revenue on money held inside them, as an incentive to save. The trade-off for that tax break is a set of limits on how much you can put in, and sometimes rules about how the money can come out.
A non-registered account has no such deal — no contribution limits, no special tax break, but full flexibility and standard taxation on any income or gains each year. Most long-term investors try to fill up their registered room first, since the tax savings there are usually worth more than the flexibility of a non-registered account.