A great uncle is the brother, or brother-in-law, of one of your grandparents. Similarly a great aunt is the sister, or sister-in-law, of one of your grandparents.
In the UK, the use of great uncle and great aunt is popular (take our favourite Womble, Great Uncle Bulgaria, for example). However there is a growing body of family historians, especially in the United States, who prefer to use the terms grand uncle and grand aunt.
The reasoning behind this is quite simple. A great uncle is the same generation as your grandfather (they are brothers). If you go back a further generation, the brother of your great grandfather is your great great uncle which can confuse people and suggest that there is an extra generation involved. Similarly, the brother of your 4x great grandfather will be your 5x great uncle.
By using the terms grand uncle and grand aunt, your 4x great grandfather's sister will be your 4x great grand aunt and that can be clearer for family historians.
However, a lot of people will have met great aunts and great uncles when they were younger and it can be hard to change the way you refer to people you once knew.
So, whether you call them great or grand, they are still family and should be celebrated.
