Yes, this is important, even though it is time consuming. The first proof is so the yeast and gluten can develop and then the second proof is so you get that amazing light and airy loaf. You don't want to over proof it though, as it will have a strong yeasty flavour. If it is under proofed then it will be a dense dough that doesn't have enough volume.  The second proof can take much longer in winter, so be aware of that. You need to look out for signs that it has proofed. The dough will have risen about 1/2 and inch above the tin and it will have formed a dome. You can also poke it. Seriously! If when you press your finger in, the dough bounces back, then it is under-proofed. On the second proof, your finger should leave an indentation if it is ready to be baked. If you dough collapses when you press it, then it is over-proofed and you will need to re-knead it and shape it and proof it again.