Alexa is the name of Amazon's virtual assistant, available through things like the Amazon Echo, the Echo Dot, and several other devices and phone/computer apps. To invoke the AI, just say "Alexa" and the device will start interacting with you.
Alexa can be added to using scripts and specialized apps called "skills". For example, I just set up my Echo Dot to play a thunderstorm when I go to sleep because I have tinnitus and the white noise covers up the ringing in my ears, allowing me to sleep. These skills can range from setting alarms, recording shopping lists when you remember you need some Tide pods and don't have a pen handy, and even playing my Sirius/XM Radio, Pandora, or Amazon Music stations.
While there are some concerns about privacy (big brother) I have no problems because I live alone. Some weeks the only verbal interactions I have are asking Alexa what the news is or what's the chance of percipitation tomorrow.
Equivalent services include Google Home, Microsoft's Cortana and Apple's Siri.