Although I don't agree with the absoluteness of the recommendation, there's a big reason why the AAP says no screen time before two years old. The best way to promote early childhood development is through high-quality interactions. These interactions are currently best provided by responsive caregivers, not technology.
But as some of the other responders have mentioned, technology can be beneficial to early childhood development if it is used to promote and enhance those high-quality interactions.
A post on Slate (When Baby Apps Actually Lead to Learning) talks about how 'baby apps' can be a positive influence on children - if parents use them as an interaction point! The apps and videos don't make a difference (and may even have a negative impact) if the parent just sets their child down in front of the screen. But if the parent engages with the child and the technology, asking questions about what's happening on the TV, helping the child to use the app and talking about what's happening, then this screen time can contribute to learning. Also another study (Skype Me! Socially Contingent Interactions Help Toddlers Learn Language -Children learn best during real-time interaction, new study finds) finds that young children can learn new vocabulary through screen time, if the people or characters on the screen are responding to children in timely and meaningful ways - aka grandparents interacting through Skype. Also there are other technologies, such as the LENA Recorder (Advanced technology to accelerate language development of children 0-5 and for research and treatment of language delays and disorders), which helps parents to see how much they're speaking with their children and how often they're engaging in back-and-forth interactions.
So in practical terms, use technology as a jumping off point for your interactions with your child and as a way to expose them to concepts they may not otherwise see in the real world.
* Does your toddler have a fascination with cars? Do a Google image search for 'cars' and instantly you have a treasure trove of pictures to talk about different types of cars, different colors, how many doors, etc.
* Is your preschooler asking "why?" too often? If you don't know the answer, admit that you don't know, and say let's figure it out together. Then use the internet to see if you can find out why.
* Did your kindergartener come home talking about a friend who just got back from a trip to Alaska? Watch videos of snow falling, and talk about what it might be like to live someplace so cold.