When a string is plucked, it vibrates back and forth between two fixed points, called the bridge and the nut. The frequency of vibration depends on the tension of the string, the mass of the string, and the length of the string.
Increasing the tension of the string increases the force pulling the string back to its equilibrium position. This causes the string to vibrate faster, which increases the frequency of the sound that is produced.
The mass of the string also affects the frequency of vibration. A heavier string will vibrate slower than a lighter string, all other things being equal.
The length of the string also affects the frequency of vibration. A longer string will vibrate slower than a shorter string, all other things being equal.
In the case of a guitar, the strings are all the same length and mass, so the only way to change the pitch of a string is to change its tension. Tightening the string increases the tension, which increases the frequency of vibration, which raises the pitch of the sound that is produced.