The aspect ratio of an image is the ratio of its width to its height. The larger the ratio, the ‘wider’ the image; the smaller the ratio, the ‘squarer’ the image.
The 1:1 aspect ratio means an image that has the same width and height, i.e. it's square. So why not say 'square'? It's because many programs have crop tools that quote specific aspect ratios like 16:9, 3:2 or 4:3, so for the sake of technical consistency square images are referred to as 1:1.