Your lowest gear will be a tiny bit lower than you have now.
Your highest gear will be quite a lot higher than you have now.
The change between cogs on the back will be slightly more gradual (assuming you have 9- or 10-speed at the moment).
The change between cogs on the front will be quite a lot more dramatic that it is at the moment and will probably involve shifting a couple of cogs in the opposite direction on the rear to compensate.
The shifting will feel great! The new 11-speed stuff works incredibly well if maintained properly (and using the proper cables – which many of the OEM bundles you see are not supplied with. If yours doesn’t come with the proper cables, do yourself a favour and get some of the genuine Shimano polymer-coated 11-speed specific cables – it makes a heck of a difference. They’re supplied with the groupset if you get an aftermarket one).