It's the world's only remaining Hindu Monarchy (Nepal is still classified as a Hindu state). The Princess is wearing a Sari & veil (the veil is common for North-Eastern brides on the subcontinent & in Fiji, as Fijian Indians hail from that area). The groom is wearing a "kurta pyjama" (tunic & trousers or Jodhpurs) and a "topee" (hat). Variations of Kurta pyjama are worn throughout the subcontinent.
Nepal's Shah family & the Princely Houses of India are a hobby of mine, so if you have any questions, I would be more than thrilled to answer them for you. FYI, the Nepalese Kings also undergo a very elaborate coronation ceremony. I posted pictures from King Birendra's coronation last year, but not sure if they're still around. It was a huge affair back in 1974, and was attended by a large contingent of foreign dignitaries. The Nepalese crown is also quite interesting.
For an introduction to the monarchy see the official page at:
www.nepalmonarchy.gov.np
And if you have any questions, I will be much obliged to try and answer them for you.
Sean