Hi R.S. Dobby, This monitor does have an HDMI input and it will be able display video from any HDMI device. I assume Apple TV has an HDMI output. However, there is one fairly important issue: this Dell monitor does NOT have a speaker. That means you will have to connect speakers or a headset to the speaker output of the monitor in order to hear any sound. It would probably be better for you to purchase a television, instead of a monitor if you want to connect Apple TV to it.
P.S. - I read the other answers below, from Chris L., and I just want to warn you again that you will not get any audio from this monitor. It does have an audio output jack, similar to what you have on a cell phone or on a airplane. You can connect ear-buds to that jack or connect some PC speakers to the jack and you will be able to hear audio. But, there is no built-in speaker.