There are many variations but a 'Hey' is a weaving in and out movement when you are dancing in a line of people.
The idea behind a 'straight hey' is:
Assume you are in a line of three. Take care to notice who is in your line. You may be dancing on the "men's" side but that does not necessarily mean that the people you meet will be men, similarly "women's" side but that does not necessarily mean that the people you meet will be women. The notes referred to here apply. The mantra is...
To describe this in detail, you start by:
If you are in the middle of the set, you have to remember to face up... the people at the bottom of the set will face up anyway as there is nowhere else reasonable to face :-)
You then dance a 'figure eight' in your line with each person doing something slightly different:
This continues, with everybody weaving 'right shoulders/left shoulders' and doing broad turns at the ends; a turn to the right at the top of the set and a turn to the left at the bottom. See this in the animation
If learning/practicing the move try it 'with hands', this both gives clear signals to the person heading towards you and helps you to remember which side you are going
In dances like the Staffordshire Knot the two sides are dancing parallel to each other. There will be the 'line of men' dancing a hey and the 'line of women'. It is quite reassuring to look across the set and see you partner dancing the same track in his/her set
There are other dances where both sides of the set dance a hey but as if there is a mirror down the centre of the set.
The Hey (or Haye) goes back a long way: