What an ICC color profile does
The numbers stored for each pixel are instructions, not colors. An ICC profile tells software how to interpret them. The same value, full red for example, is a more saturated red in a wide-gamut space than in sRGB. Without a profile, software has to guess, and almost always assumes sRGB. The checker reads the profile's own name, such as sRGB IEC61966-2.1 or Display P3, or reports None embedded (sRGB assumed).
sRGB, Display P3 and Adobe RGB
sRGB is the long-standing standard for the web, most monitors and most consumer printing services. Display P3 covers a wider range of colors, especially reds and greens, and is used by recent iPhones and Macs for photos and screenshots. Adobe RGB is another wide space, stronger in greens and cyans, used by many cameras and in professional photo and print workflows.
Why colors shift between apps
The most common cause is a profile being stripped. If a Display P3 photo loses its profile on export or upload, software reads its numbers as sRGB and the picture looks duller or slightly off. Apps that aren't color managed ignore profiles altogether, so the same file can look different in a browser, an image viewer and an office document.
For the web, an image in sRGB, or one that keeps its profile embedded, displays most consistently. The resize, compress and convert tools on this site keep the ICC profile when they process a file. This checker only reports the profile; it doesn't convert between color spaces.
Reading the color mode
The color mode shows how pixels are stored. RGB is standard color, RGBA adds an alpha channel for transparency, L is grayscale, P is a limited palette (indexed color, common in GIF and small PNGs) and CMYK is a print format. 16-bit modes appear as I;16.