In the context of premises liability law, “notice” refers to whether the owner/possessor knew about the hazard that caused your accident, before the accident occurred. If the owner had this “notice” knowledge, then he/she can be held liable for your injuries. When the owner actually has knowledge of the hazard, this is called “actual notice”.
Also, did the owner have an opportunity to remedy the hazard? One can easily visualize an accident in a supermarket aisle, involving a spill that the store manager knew about, and already had a cleaning crew dispatched to clean it up, when the accident happened.
There is potential liability as well, for “constructive notice” of a hazard, referring to knowledge the owner should have had, if he/she were paying reasonable attention to the property. How do we know what knowledge the owner “should have had”? By proving that the hazard existed for a significant period of time. You will need to be able to give detailed factual descriptions of the hazard, that will help show its “age”.