The imitator can be compared to a shadow. It can't capture nor can it be captured nor give check. Whenever a pieces moves, the imitator moves exactly in the same way. Of course, there are some restrictions.
An imitator can't cross an occupied square except when it imitates a hopper and also has to have a hurdle. A move is illegal if it can't be accompanied by a legal move of an imitator, i.e. putting it on an occupied square (after the piece has moved) or off the board.
Normally, an imitator imitates moves of both sides, but you can also declare it to do so only when either White or Black moves. In general, the symbol is a black circle.
With more than one imitator on the board, a move is only legal, if all of them can imitate it. The promotion to an imitator is legal, but can be excluded.
The following quite simple diagram demonstrates the effect an imitator has.
a) Black to move:
You can see that the imitator move is written in (round) brackets.
The imitator shields the white king from checks. Therefore, a king move puts White in check.
Moves like Ra7 or Rh5 or Ke7 are not allowed as the white king blocks the imitator.
Castling long is not possible, because the first part is the king move which is not allowed due to the position of the imitator. On the other hand, castling short works, as the imitator goes to c6 after the king move and returns to a6 after the rook move.
b) White to move:
Observe that the white knight can't move at all. It's pinned, for any move would put the white king in check which is not allowed.
Here's a composition which is easy to understand:
|Europe Echecs 1966|
1. Kh2 (Ic5)! puts Black in Zugzwang:
1. - Na3 (Ia4)+ 2. Nh7 (Ic5)#
1. - Nb2 (Ib3)+ 2. Ng8 (Ic5)#
1. - Nd2 (Id3)+ 2. Ne8 (Ic5)#
1. - Ne3 (Ie4)+ 2. Nd7 (Ic5)#
1. - Ne5 (Ie6)+ 2. Nd5 (Ic5)#
1. - Nd6 (Id7)+ 2. Ne4 (Ic5)#
1. - Nb6 (Ib7)+ 2. Ng4 (Ic5)#
1. - Na5 (Ia6)+ 2. Nh5 (Ic5)#
The black pawn is blocked and any bishop move would put the black king in check, so only the black knight can move. We see a black knight wheel answered with a corresponding white knight wheel to put the imitator back to c5, so that the white king is not in check whereas its black adversary is and can't escape.