Tack against prevailing winds is a nautical sailing term.
Sailing against the wind is very difficult for a sailing ship – the force of the wind prevents the sails from moving the ship in that direction.
Sails on sailboats can be shifted so that they can still get motive thrust from the wind within a range of degrees towards the wind, though (it depends on ship and sail design). So an old sailing trick is to sail at an angle as close to the wind you can manage – and then after a little bit switch course to the mirror opposite angle against the wind. The net result is a zigzag course roughly against the prevailing wind. That zigzagging known as "Tacking".
Its certainly slower than sailing with the wind – but it does allow you to make headway if you need to be traveling in the direction the wind is blowing from.
20Note: "tack against" is almost always paired with "wind", as in your quote. – CJ Dennis – 2019-01-28T12:32:00.390