what exactly are 'Evasive Manueavers'?

[CAPTRousseau]

Evasive action in naval parlance, I believe, refers to random serpentine maneuvers, where the ship makes sudden turns in a snakelike pattern so as to be an unpredictable target.

Not always just random maneuvers, there's also a technique where you "chase the splashes," in order to throw off the aim. The enemy will be adjusting their fire based on where their last shot landed

 

[Capn Nick]

I thought it was to buy time more than avoid getting hit altogether. They either have a targeting computer or, when that is down, they are "locking on" manually. Seems like, especially between two comparable ships, making it take 12 seconds to track and hit you rather than say, 3, would be an advantage. I think somebody else mentioned it above. The "shots not fired" factor.

 

[Marsden]

"I'm issuing an order now to make it appear I'm thinking tactically, but we're really just going to sit here because the plot demands we die in the most rapid way possible."

Ah, yes, the Estaban Maneuver! Required reading at the Academy.