Icons are created in different sizes (X pixels x Y pixels, although pixels around the periphery of the image are usually transparent so it looks like a shape other than a rectangle). The sharpest icons will come from selecting a large icon size and viewing it unchanged (set the desktop to use large icons or substitute third party icons that are bigger).
The alternative is to create a new icon by enlarging an existing one or viewing an existing icon magnified. These are essentially equivalent to each other in terms of appearance.
If you want to view the icon larger than its actual size, there are three common methods of expanding it. One is to repeat each pixel several times, so one original pixel would be displayed as 2x2 of the same pixel (doing that to every pixel doubles the size of the icon in each direction), or 3x3 of the same pixel (triples the size in each direction). This only works for whole multiples of size. When you do this, the enlarged "pixels" look crude, like blocks, and this is called "pixelation". This will look as sharp as the original, just cruder.
If you want something in-between whole multiples of size or want something that doesn't look pixelated, you pick a size or multiplier and that determines the number of pixels in each direction. The content of each pixel is then generated by one of several methods.
The simplest is averaging or interpolating from adjacent pixels in the original. This is how DPI scaling and zooming are done. This gives a smoother image, but detail isn't as sharp because edges get spread out or averaged away; it can look blurry.
The other common approach is more complicated and is essentially an optical illusion. It uses a process called dithering. Dithering is used to fake colors, like when you need to convert a photo that has 256 shades of each component color to a format that has a total of only 256 colors. It tricks your eye by putting pixels of available colors that are similar to what is required in close proximity and your eye averages them. Pixels can, instead, be used to enhance edges or the appearance of detail at the expense of color accuracy.
Working with a photo, this technique can produce results that are almost as good as the original using a fraction of the colors (and file size). Starting with an icon isn't much to work with and the results would vary with the nature of the image. It would likely be sharper than DPI scaling, but could look "odd" at that scale. This technique would be done using an image editor to create a new icon.
An image editor could also be used to enlarge an icon by the same method as DPI scaling and then make it look sharper artificially (and save it as a new icon). Actually, if you use an image editor, there are likely to be resizing algorithms available that do the equivalent of averaging or interpolating but use more complicated functions and produce sharper enlargements to start with. Basic techniques for artificially enhancing sharpness involve increasing the contrast in general, or increasing the contrast along edges by making the dark side darker and the light side lighter.
So those are basically the options. If you can't achieve what you want through a larger original icon, you have to decide which tradeoff you find the least objectionable.