In addition to the examples provided by others here, this phrase is also used in Star Trek 3, when Kirk's skeleton crew assembles in The Enterprise before they steal the ship, where each member of the crew signals their intention to join Kirk and McCoy on the rescue mission. Sulu asks for the ship's course, Chekov says they are wasting time even discussing it, and Scotty asks Kirk to 'give the word'.

All these instances, the sense in which it is used appears to mean to 'give an order', which is basically the same as its meaning in everyday, non-nautical language, as in 'when you give the word I'll release the final report to the press'.

This is why he follows it up with 'Warp speed' in your example. Warp speed is the order.

In addition to the examples provided by others here, this phrase is also used in Star Trek 3, when Kirk's skeleton crew assembles in The Enterprise before they steal the ship, where each member of the crew signals their intention to join Kirk and McCoy on the rescue mission. Sulu asks for the ship's course, Chekov says they are wasting time even discussing it, and Scotty asks Kirk to 'give the word'.

All these instances, the sense in which it is used appears to mean to 'give an order', which is basically the same as its meaning in everyday, non-nautical language, as in 'when you give the word I'll release the final report to the press'.

This is why he follows it up with 'Warp speed' in your example. Warp speed is the order.

The other similar but subtly different sense this phrase has in everyday language is to 'give the go-ahead', which could also arguably apply in the example where Kirk is giving his verdict after carrying out the inspection on the engineering deck.