This is a great question, because the default answer is usually wrong for 99% of applications. The default answer is: to avoid reflections and other problems with high frequency signals.
The default answer assumes that you are dealing with very high frequency signals - signals with a wavelength that is small enough to fit a couple of times in your trace. When you regard such a signal as a wave, when it hits the end of a trace or a 90 degree corner, it gets reflected back and causes destructive interference with itself, attenuating the signal.
However, almost all signals you will ever route through a PCB are either DC or - in terms of these kinds of problems - very low frequency. Even 1MHz is a very low frequency and you will not run into these kinds of problems. It's 100+ MHz that starts entering into routing problems. A great example of signals that benefit from clean layout in this respect are serial buses: PCIe, USB 2.0+, etc.
This does not mean that it's good practice to make sharp corners all over the place. There are a couple of reasons why you even want DC signals and basically all your routing to have nice 45 degree angles or rounded corners:
- First of all, board area use. 90 degree angles or worse still: more than 90 degree sharp corners will always cause longer traces (higher impedance, more copper use) than traces that try to snake around obstacles. And often, your board size is limited, so you want to use as much area for the actual components, not the traces in between.
- Cleanliness. A clean, nice-looking board layout is easier to optimize, transfer and troubleshoot.
- Manufacturability. This is much less of a concern than in the past, but still something to consider if you plan on prototyping this on a hand-etched or milled PCB. Sharp corners tend to get loose when milled or get under-etched when using crude manual etching methods. Fluent lines are easier to produce.
However, if you know what you are doing, don't hesitate to use sharp corners when you need them. As always: strict rules are for beginners and dumb people, once you know what you are doing you know when it's alright to deviate from the rules.
Many switched regulators include example layouts, such as the suggested alternative part TPS40200. http://www.ti.com/lit/ds/symlink/tps40200.pdf . The datasheet shows the evaluation module layout and a suggested layout. If you copy that layout then your circuit will probably work.
One thing I found interesting is that switched regulator layouts tend to use copper fills instead of traces to connect high-current paths and simultaneously provide some heat sinking. For example in your layout C10-C12 and the large rectangular component could sit on top of a solid rectangle of copper. Keep in mind that the electrons will take the lowest impedance path.
Best Answer
The important thing is not so much track width (which must be rated for current, not voltage) but track spacing. See Clearance and Creepage.
For example, if you rotate the relay 180 degrees, you can keep the coil driving pins closer to the Arduino and not have to route them so close to the mains. You might also consider putting low voltage and high voltage on the opposite sides of the PCB.
(do you have enough power from the Arduino for that relay coil? Do you need a flyback diode?)