When your strategy hinges more upon breaking through or holding a position than what the loses you'll take from it looks like, such as breaching an entrenched riverline or a defended position during a naval invasion, such as attacking Gibraltar with a naval invasion.
Last stand is useful in situations where you'll be in a lot worse strategic position afterwards if you lose a battle, rather than just a smaller tactical setback. This is e.g if you need to prevent an enemy from encircling you, or if you're defending a port against a naval invasion that will stop dead in it's tracks if it fails to capture a port.
Do be warned, using these abilities is considered off limits in some MP games, so you'll have to check with their particular rule set in use.