I'm sorry if this sounds like a silly question but I don't understand how measuring the location of a star would help in sea navigation.
Measuring the angle to a known star allows the navigator to calculate the latitude of the ship in the absence of any visible (known) landmarks.
Since they would know (or refer to an almanac) the celestial latitude (declination) or altitude of the star at their home port or some other known port, they can measure the position of the star and take the difference between the measurement and the reference to calculate their latitude at sea.
For example, if their home port were located at 54°N then the angle from the horizon to Polaris would be 54°. If they take a measurement of Polaris while at sea and find it to be 30° above the horizon then they know that they are 24° farther south, i.e. latitude 30°.
Similarly, if there were a star that is directly overhead (90° from the horizon) when it transits the celestial meridian at home, then they know that that star has a declination of 54°. If they take a measurement of it while at sea and find it to be 6° north of zenith (84° from the horizon) then they know that they are 6° south of home.
From all of this, knowing the date lets them calculate the sunrise and sunset times, and if they have an accurate clock they can work out their longitude. In the past, longitude was a bit more guesswork as clocks were not all that accurate at sea.