Essentially, a DisplayPort is a digital display interface primarily used to connect a video source to a display device (mostly monitors). It also carries other forms of data such as audio, USB, etc.
With televisions, HDMI is the most common connector. But if you want to connect a computer to your TV (or you've got a new computer monitor), the options tend to be HDMI, DisplayPort, DVI, and ...
A common problem you may encounter with your DisplayPort, which connects the monitor to a graphics card, is called Link Failure. This is when that connection fails. It mainly happens with AMD graphics ...