Both words mean "circle", although 丸 has also other meanings. But what's the nuance between them?
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輪【わ】 is closer to ring or loop rather than circle. A 輪 doesn't necessarily be precisely circular, as long as it forms a loop. For example, the Japanese word for rubber band is 輪ゴム; it can deform and have a triangular shape.
丸【まる】 is a circle typically drawn on a paper, or displayed on a screen (The circle symbol (○) is called 丸). The important nuance of 丸 is that it must not have a sharp corner/edge. There's an i-adjective 丸い which refers to any round, cornerless objects. We can even say 丸い三角 (rounded triangle). And 丸 also means 'correct'.
And one more:
円【えん】: circle as defined in geometry, which is perfectly-round and should be drawn by a compass.
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1So 輪 would be something like a "turn"? I.e. something that "runs" a path then connects reaching the starting point? – Yuuza Sep 30 '15 at 08:23
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1Yes, I think that's the important nuance of 輪 (cf. メビウスの輪) – naruto Sep 30 '15 at 08:28
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丸い三角 = "rounded triangle", right? – senshin Sep 30 '15 at 18:12