2D Wavelet Transform Explanation
You can notice that:


the top left looks like the original image, albeit smaller
the top right shows mainly horizontal features
the  bottom left shows vertical trends
the  bottom right is much less clear


What you show "is not wavelets" per se. It is another image, normally with the size of the original one, with four quadrants. However, it illustrates some wavelet features. The top left is a coarse approximation of the image, resulting from filtering and downsampling,  obtained from a scaling function. The three others are details, with at least one high pass component. In the classical version, this image combines low- and high-pass on rows, and the same on columns, each followed by downsampling on both directions, which explains the above items. If you iterate the process on the low-pass image, under some conditions, you get a separable two-dimensional wavelet transformation. The key point is that in your image, all the original information remains.