Open an image and then go to the mesh warp tool in the tools panel of Affinity Photo and then you will see a bounding box added to the image and this can be used to distort the image, you can hover over the lines and drag in and out and distort the design.
You can use this is destination mode that gives an instant feedback to the distortion but if you select the source mode then the controls are the same as the destination but nothing will change as you distort and move the lines etc but you will see the result of the extreme distortion after you click apply. The destination option is the default.
You can also add additional points to distort the design buy double clicking on the document. You can then add a move point to move the points as well and this works best once you have added multiple mesh points via the double click.
Those points can be dragged and manipulated via their anchor as well as direction points to create sharp or smooth designs and you can also use the convert buttons along the control bar to modify these for even more amazing designs. If you add lots and lots of points to the image, then the distortion can be localized to a very small area of the art. Once you are happy with the preview, click OK. You may like to tryout different options such nearest pixel etc as well.
You can also add a selection to the image using the rectangular, elliptical etc tools and once you have those, you can still use the effect but the manipulation of the pixels is then only applied to that area of the selection and not the rest of the image. You can also use a selection to copy and paste part of the image and create a layer and then use it to distort that layer instead of the main image
You can also use it with pattern layers, use it to distort shapes as well as artistic text and frame text and more.