What to see
Above you see a sort of 3×3 checkboard delimited by wavy coloured borders. You may also see that every other square is subtly coloured, for me they appear orange-ish. As you already guess: this is an illusion, all squares have a totally white background.
What to do
There a lots of settings you could play with. Start with the checkbox next to the purple colour – the orange lines are still there, but the tint of the square is gone! When the linewidths are reduced to 1 with their stepper you can also appreciate that all squares are, in fact, white. You can exchange the colours with the button “↔︎” between the colour selectors – the illusory colours exchange place. The colours can also be changed, but try desaturating them first with the slider below the colour selector: I'm impressed that at low saturation the induced illusory colours are already quite pronounced.
This rather beautiful phenomenon is called “Watercolor Illusion” and was discovered by Baingio Pinna (1987). But how does it come about? Scientifically this would be described as “ a phenomenon of long-range color assimilation occurring when a dark chromatic contour delineating a figure is flanked on the inside by a brighter chromatic contour; the brighter color spreads into the entire enclosed area. Yes, but not very intuitive, and I would venture to say that it's not really understood… See also the pertinent Wikipedia entry. I assume that centuries ago people who were experienced in map colouring already knew about this.
Pinna B (1987). Un effetto di colorazione. In: Majer V, Maeran M & Santinello M (Eds) Il laboratorio e la città. XXI Congresso degli Psicologi Italiani (pp 158). Milano: Società Italiana di Psicologia.
Pinna B, Brelstaff G, Spillmann L (2001) Surface color from boundaries: a new 'watercolor' illusion. Vision Res 41:2669-2676
Pinna B, Werner JS, Spillmann L (2003) The watercolor effect: a new principle of grouping and figure-ground organization. Vision Res 43:43–52
Devinck F, Hardy JL, Delahunt PB, Spillman L, Werner JS (2006) Illusory spreading of watercolor. Journal of Vision 6:625–633
Gerardin P, Devinck F, Dojat M, Knobloch K (2014) Contributions of contour frequency, amplitude, and luminance to the watercolor effect estimated by conjoint measurement. JOV 14(4):9, 1–15