Welcome to the Apple community.
Are you sure that the video you are trying to play is compatible with the Apple TV, simply because it will play in iTunes does not ensure it is.
Video formats supported
H.264 video up to 1080p, 30 frames per second, High or Main Profile level 4.0 or lower, Baseline profile level 3.0 or lower with AAC-LC audio up to 160 Kbps per channel, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats
- MPEG-4 video up to 2.5 Mbps, 640 by 480 pixels, 30 frames per second, Simple Profile with AAC-LC audio up to 160 Kbps, 48kHz, stereo audio in .m4v, .mp4, and .mov file formats
- Motion JPEG (M-JPEG) up to 35 Mbps, 1280 by 720 pixels, 30 frames per second, audio in ulaw, PCM stereo audio in .avi file format
Audio formats supported
HE-AAC (V1), AAC (16 to 320 Kbps), protected AAC (from iTunes Store), MP3 (16 to 320 Kbps), MP3 VBR, Audible (formats 2, 3, and 4), Apple Lossless, AIFF, and WAV; Dolby Digital 5.1 surround sound pass-through
Photo formats
JPEG, GIF, TIFF.