In more detail
Pixel count is fixed by the file or the screen; physical size depends on how densely the pixels are spread. For a screen, density is the diagonal in pixels divided by the diagonal in inches: √(width² + height²) ÷ diagonal. For a print, the required pixels are the print size multiplied by the PPI; around 300 ppi is the usual target for photos viewed up close, and less is fine for posters seen from a distance.
Why it matters
A photo that looks sharp on a phone can print blurry if it lacks the pixels. Changing the "DPI" value in a file's metadata only changes its suggested print size; it does not add or remove a single pixel. Enlarging a small image cannot recover detail that was never captured, and more pixels do not improve a photo taken out of focus or in poor light.
Example
A 6 × 4 inch print at 300 ppi needs 1800 × 1200 pixels. A 27 inch 2560 × 1440 monitor has √(2560² + 1440²) ÷ 27 ≈ 109 ppi, while a 27 inch 3840 × 2160 (4K) monitor reaches about 163 ppi, so the same text looks noticeably finer.
Common confusion
PPI describes pixels in an image or screen; DPI strictly describes the ink dots a printer lays down, though the two are often used interchangeably. Resolution is a size, not a shape: see Aspect ratio.