Your current lens belongs to the category of standard zoom lens. If you zoom out all the way 18mm is the maximum wide it can get (for big group pic / landscapes) and if you zoom in all the way it can go up to 55mm (for close-up of far objects). The crop factor for your cam is 1.5x so the actual 35mm equivalent range is 18x1.5 - 55x1.5 = 27mm-82.5mm.
It means if you put your lens on a full frame nikon cam it will give you more wider bigger view (18 instead of 27) which you can see in pic below.
You can also calculate your zoom range from these numbers:
55/18 = 3x zoom or 82.5/27 = 3x zoom
Your Sony cam has two components in that number. First one 2.8-5.8 represents the f number range. If you use 2.8 then background will be more blur and only some area of your screen will be in focus and more light can go in your lens. If you use 5.8 then most of the screen will be in focus and less light will go to your lens.
Second is focal length same as your nikon lens. 5.35-21.4
This is equal to 30-120mm on 35mm equivalent full frame cameras.
Zoom range would be:
21.4/5.35 = 4x zoom or 120/30 = 4x zoom
35mm equivalent is the sensor size or size of view field the big professional full frame cameras cover. All other cameras cover some part of that so we compare focal length by converting it how it would look like at full frame.
This below pic gives some idea of nikon crop of 1.5 compared to full frame 35mm cameras: