Do i need a capture card?

I see the the Lenovo IdeaPad Y510p has an HDMI port on it. Do I still need a capture card or can't I just connect my Xbox to the laptop and thats that?

The HDMI port on your computer is outbound - from computer to monitor - only. If you want to capture game play, you need some sort of capture card or analog/digital converter (Blackmagic Design, ElGato, Thompson/Grass Valley/Canopus… Many others)…