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.
When referring to Intel's integrated graphics, it would more properly translate to "Highly Deficient Graphics," as it is unable to play many modern games, and those only at lowest settings. Although also not considered a gaming card, even a GT440 would be much more powerful, and a HD5670 would be another giant step up from that.