Flight and trip delay insurance reimburses you for necessary and reasonable accommodations, restaurant expenses, and sundry items that results from a delayed flight or trip. This will typically only kick in based on how many hours you've been delayed and whether or not an alternative mode of transportation was made available to you (such as an alternative flight). There are some exceptions and the exact benefits will vary between card providers.
Flight and trip delays can be expensive depending on your trip itinerary. It could cause you to miss a connecting flight or transportation that you've booked and mapped out. Sure, most airlines will typically try to make up for it by putting you on the next flight, but what if that flight you missed was the last one to that destination? Now you're looking at possibly having to book a hotel, spend extra money on food, and deal with other unplanned expenses. This is where flight and trip delay insurance comes in handy. You can be reimbursed for unforeseen issues such as this and save yourself some money.