This is the term used for making progress in the direction that the wind is coming from. You cannot sail directly into the wind because your sails will not fill. Therefore you zig-zag towards the wind in a series of 'tacks'. Each tack will help you make progress in a windward direction.
If you are sailing with the wind coming from your right hand side, you are on starboard tack (and in racing you have right of way over boats on port tack) and if the wind is coming from your left hand side you are on port tack.
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