The app is Sleep Cycle Alarm Clock, and I love it. It's caused a minor miracle in my life which I can't really attribute to anything else! You plug in your phone, turn on the app and set the alarm, and place it on the corner of your bed next to your pillow. It detects your movements and, thereby, your sleep cycle so that it can wake you when you are in a lighter phase of sleep. The default is 30 minutes before the time you set, but you can change that.
Back when I was just waking to the alarm at a set time, I was extremely groggy and took a long time to wake up. I could hardly function. Now, I wake up, and I may not be super-energetic, but I'm fine---I can walk, talk, work out, and generally be a decent human in the mornings!
The best example of how well this works is how I feel on Friday mornings. We go to Eucharistic Adoration at 4:00 a.m., so we get up at 3:40 (which is generally my deepest sleep phase of the night!), and we're back in bed by 5:15. Well, I could stay in bed (during the summer) until 8:00 a.m. and still be dead until noon. Now, I need to be up for school, so I set my alarm for 6:30, or even 6:00, and it manages to wake me at a good time, so that I am fully functional on Fridays, too! That is the most amazing thing to me!
It's not likely to work very well with a toddler in your bed, though I am pretty sure it must pick up some of my husband's movements, and it hasn't caused a problem. Generally, the graph matches how I felt about my nightwaking. Last night (above) was not a good night. Not enough deep sleep and too much tossing and turning. Monday, however, was awesome. I have a tendency to wake up every night around midnight, it seems. But I already knew that. ;-)
Let me tell you, this was totally worth the $1.99 expense. Now I can buy less coffee. :-)