Stamina, as shown in Narwhale.io, is the amount of times you are able to charge your tusk into an opponent or an open area. This can be upgraded up to 4 times, and the maximum amount of charges is 5, which is very rarely achieved. It is important to note that the higher the level of stamina that your are trying to achieve reaches the more stamina upgrades it takes to achieve the next level.
One way to save stamina is by using the tactical defense manoeuvre (right click with the mouse). This is basically a backward dash and cannot kill other narwhales, but is useful for defense, getting out of tricky situations and travelling if you are a pro. Tactical defense does use stamina, just as a normal dash, but the stamina recharges much quicker allowing for much more options in the field.
The recharge takes 2 - 3 seconds to fully restore the charge. The stamina regen upgrade allows for a faster recharge, especially on the higher levels.
Charging is the only way to kill an opponent.