When I export my Illustrator file to PNG it appears blurry when I zoom to 120%.
Assuming the basics are needed:
Export to bitmap such as png, jpg, bmp, tif may look same as the original as long as it's not zoomed in (=enlargened). All pixels that Illustrator puts onto your screen are still available in the bitmap when you do not zoom in.
If you zoom in your vector art in Illustrator, the result seems still sharp because Illustrator has all info needed to produce more pixels into right places onto your screen.
But zooming in the exported bitmap is different. Your bitmap image software, let's say Photoshop, knows nothing about the curves and fonts that are used in the original vector art file. Photoshop tries to guess the missing pixel values that are needed between the old pixels when image is stretched to be bigger.
Generally that guessing process (=interpolating) chooses the average, when a new pixel must be inserted between two old pixels with differet colors.
The average should not be taken literally because color border edges and gradients can be enlargened more smoothly, if the interpolation process also looks the the trends, how the borders and the color changes really are lining from few pixels further. This is called "anti aliasing". Without anti-aliasing the zooming in makes color borders and gradients in your bitmap more rough (=jaggy). That also is an error.
Anyway, the guess is a guess and that makes the enlargened image fuzzy or jaggy. To keep your exported bitmaps sharp DO NOT enlarge them in bitmap mode. Choose allways so big pixel dimensions for the export that only zoom out (=shrinkening) may be needed. That can be done much more accurately without quessing.
In Photoshop there exist some advanced resampling modes in the dialog where image size can be cahanged. One of them is "Bicubic". This is for retaining smoothness. There are even advanced 3rd party sharpness and smoothness retaining photo enlargenig plugins. But even at its best any enlargening method cannot be a substitute for having your bitmaps with large enough pixel dimensions from the very beginning.