multi: true means that one provider token provides an array of elements. For example all directives for router support routerLink, router-outlet are provided by ROUTER_DIRECTIVES.
If a new provider is registered with the token ROUTER_DIRECTIVES, then it overrides the previously registered directives. If multi: true (on the first registered and the new provider) is set, the new directives are added to the previously registered directives instead of overriding.
When ROUTER_DIRECTIVES is injected (constructor(@Inject(ROUTER_DIRECTIVES) directives) {}) an array of directive instances is injected. It usually doesn’t make sense to inject ROUTER_DIRECTIVES. I used it just as an example because it is multi: true.