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What is the meaning of the phrase "the same player has the move" in the sentence below

"Two positions are by definition "the same" if the same types of pieces occupy the same squares, the same player has the move, the remaining castling rights are the same and the possibility to capture en passant is the same." The sentence is taken from https://en.wikipedia.org/wiki/Threefold_repetition.

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In short, it means that either both positions must be "white to move" (white's turn) or both positions must be "black to move (black's turn). If the pieces are in the same places, but one position is white to move and one position is black to move, they're different positions.

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The Wikipedia editors got that from article (.2 the FIDE Laws of Chress.

This is what it says:

9.2.1 The game is drawn, upon a correct claim by a player having the move, when the same position for at least the third time (not necessarily by a repetition of moves):
9.2.1.1 is about to appear, if he first writes his move, which cannot be changed, on his scoresheet and declares to the arbiter his intention to make this move, or
9.2.1.2 has just appeared, and the player claiming the draw has the move.
9.2.2 Positions are considered the same if and only if the same player has the move, pieces of the same kind and colour occupy the same squares and the possible moves of all the pieces of both players are the same. Thus positions are not the same if:

9.2.2.1 at the start of the sequence a pawn could have been captured en passant
9.2.2.2 a king had castling rights with a rook that has not been moved, but forfeited these after moving. The castling rights are lost only after the king or rook is moved.

So, what this is saying is that when it is your move, instead of making a move, you can claim a draw provided the position is a third repetition or you could make a move to make it the third repetition of the same position.

What you see in the above description is that to qualify as a repetition of the position every single aspect of the position must be exactly the same including the person to move.

The significance of "the same player has the move" is that if you are claiming that the position in front of you is a third repetition then on each of the two previous repetition positions it was your move. If you are claiming that by playing a particular move you can repeat the position for the third time then to be true the position which would arise with your opponent to move was identical to the previous two repetition positions and on each it was your opponent's turn to move.

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