Vinyasa Yoga refers to a style of yoga that links the breath and a number of poses into a sequence, such as the Sun Salutation shown in the image above.
These sequences are often practised to music and may be repeated a number of times in a class. Once you become accustomed to the sequence, and no longer have to worry about where to put your various limbs and when, they have a dance-like quality that people find very relaxing and enjoyable.
The Sun Salutation, or Surya Namaskar, is one of the most common vinyasas practised in yoga today.
There are a number of different variations on this sequence and a good vinyasa teacher will also create their own sequences.