If you are like many people these days you use your iPhone for many tasks that require you to unlock the phone, open an app and input some info. You can use Siri from the lock screen to accomplish many of these mundane tasks much quicker. Just long hold your Home button until Siri comes up and speak your command. Alternatively, if your iPhone is plugged in to a charger, you can just say "Hey Siri" to launch Siri instead of holding the home button.
1) I often use it was cooking for setting timers. "Hey Siri, set timer for 20 minutes" is a lot faster than unlocking the phone, launching the Clock app and starting a timer.
2) In the car, if a text message comes in, since I obviously won't be looking at my phone while driving, I can say "Hey Siri, read me my text messages" and Siri will read the messages. You can also reply.
3) When I leave the dentist or other appointment, they often have given me a card with my next appointment on it. To add it to my Calendar, just say "Add appointment for dentist on [date] at [time].
4) When I get up in the morning, to check the weather, I just say "Hey Siri, what's the high for today?" or "Is it going to rain?" etc.
5) in the car, if I need to make a call, I can just say "hey siri, call home" (or whatever contact I need).
6) to get directions to an address in your contacts, just say "Hey Siri, take to me Allison's house".