Well, HD means high definition which today means a 1080p resolution. 720p is also hi def, but mostly when referring to computers people are talking about 1080p, or 1920 X 1080 pixels.
HD Graphics just mean capable of rendering hi def content; games movies, etc.
You could be referring to the HD3000 graphics that come with the core i5 CPU's. Which is an integrated solution, it does not require a seperate card to display graphics.
1GB Graphics simply means that whatever graphics we are talking about, integrated or discrete there is 1 Gigabyte of video memory available to the GPU. But typically when you see 1GB Graphics, it means a video card with its own memory.