the order of reflection

In Bragg's law, n lambda = 2 d sin theta, the little integer n is the order of reflection. It counts how many whole wavelengths of extra path separate waves bouncing off neighbouring planes. n = 1 is first order: neighbouring planes differ by exactly one wavelength. n = 2 is second order: they differ by two whole wavelengths, and so on. Each higher order is another way the same family of planes can produce a bright beam, at a steeper angle.

Why do higher orders sit at larger angles? Because to fit two whole wavelengths of path difference instead of one, the geometry needs a bigger sin theta, hence a bigger theta. For the same planes you therefore see a series of reflections marching out to larger angles: first order, second order, third order. Each is progressively weaker, partly because the atomic scattering factor falls off with angle. There is a ceiling: since sin theta cannot exceed 1, only orders with n lambda < 2 d can ever appear.

Crystallographers have a tidy habit that makes n almost disappear. Rather than writing 'second-order reflection from the (100) planes', they rewrite 2 lambda = 2 d_100 sin theta as lambda = 2 (d_100 / 2) sin theta and relabel it the first-order reflection from planes of spacing d_100 / 2 — that is, the (200) planes. So the nth order of (hkl) becomes the first order of (nh nk nl), and every reflection can be given a single (hkl) label with n = 1 understood. This is why diffraction patterns are indexed (100), (200), (300), ... rather than 'first, second, third order of (100)'.