How to get more Refresh Rate on my monitor?

I have a Intel HD Graphics and when I go to Screen Resolution > Advanced Settings > Monitor. And I click on the Hertz tab,. All I saw was 60Hrtz. How do I get more than that? I have Minecraft and it is really lagging and I need less lag.

Added (1). I have just a Monitor. Not a giant box that connects to a Monitor.

The lag your getting is because of the Intel Graphics card you have, nothing to do with refresh rate or the monitor.

Refresh rate doesn't have anything to do with the lag you're getting when playing Minecraft

Intel graphics card can't handle high-end games. Consider upgrading to better ATI Radeon or NVIDIA GeForce dedicated graphics card

If you don't have a "giant box" that connects to a monitor, then you must have something that does connect to it. If you don't then you don't have anything on the screen and you don't have "Intel HD Graphics".
If you won't tell what you do have, no one here can help very much.