The memory footprint of images goes up exponentially as they get larger. A 100x100 image has 10,000 pixels, while a 1000x1000 image has 1,000,000 pixels.
Note that for mobile devices especially, even though the resolution on modern devices is as high as monitors, the dpi density is also much higher. Basically even though it is high resolution, the physical screen size is still very very small. You can use much lower resolution textures, with scaling, and it will be much harder for an eye to discern the difference on a mobile screen versus a monitor, even if both the monitor and mobile device have similar resolutions.
To further optimize, similar texturing techniques to 3d can be done in 2d with repeating backgrounds and the canvas plugin (optionally with effects as shaders). Use the canvas plugin to draw the shape, and layered repeating backgrounds to texture large areas of it.
Edit: As with tiled backgrounds, by extension the 9-patch object can also be used in certain situations to lower memory use significantly.
More traditionally, 2d games make very heavy use of tilemaps to reuse a set of textures over large areas. When that is still not enough, different tilesets assets are loaded and unloaded as needed (via layouts in Construct). This is usually done when areas don't have much in common and assets can't be easily reused or shared between the two, such as different biomes.
Note that tilemaps are not only useful for terrain. With a little creativity, they can be applied in other situations as well.