For web use, pixels are all that matter. The image needs to be X pixels by Y pixels, and that’s all we really need to know.
The resolution (usually expressed in dots per inch, dpi) is not the same thing as the pixel size but says something important about how the image is displayed, on screen or on paper. For instance, an image 250 x 250 px may be displayed on screen at 96 or 120 dpi according to the device, making it (roughly) two and a half or two inches (i.e. 60 or 50mm) square respectively; or it may be printed at 300dpi, making it less than one inch (25mm) square.
File size (usually expressed in kilobytes or megabytes, KB or MB) is related to pixel size but again doesn’t matter much for display purposes. For a given pixel size, a larger file will appear as a better quality image but will take longer to load.