I come from the mindset that no law is strictly physical/spiritual. They blur into one another and provide benefits which merge those aspects.

Fasting is powerful in a spiritual sense because you are choosing to take control of a baser instinct. Hunger is as basic as breathing or sleepiness, so by choosing to overrule that instinct in reflection of a spiritual observance/exercise you are strengthening your divine traits and suppressing primal traits. Torah teaches that the Nefesh HaBehamit "animal soul" is in conflict with our Nefesh Ha'elokit (divine soul)

These comprise two different sections of our soul which are in a battle for control. By doing spiritual exercises (such as fasting) you can drive down the animalistic urges and raise yourself to a higher state of craving. You can move from craving that which is harmful to craving that which is beneficial if you practice and focus your time/energy. Fasting is just one of those exercises.

Fasting also has a symbolism associated with it in relation to the pain that hunger causes. When we observe Tisha B'Av (just one example) we fast. This holiday is a memorial in reflection various wrongs of Jewish history. One of the main reflections is on the loss of the holy temples (first and second).

This hunger pain is symbolic of the spiritual pain of our people. We sit in hunger and reflect on this pain and attach that pain to the wrongs and errors of Jewish history. By doing that, we take an impersonal history and we connect to it. I can't know what it was like to lose the holy temple because I never had the holy temple. That doesn't mean I can't reflect on what that loss has done to my ancestors and my peers of today.

By connecting the pain of our people to a pain which is rooted in our biology, we groom ourselves to make the suffering of our past a part of who we are. That strengthens us and drives us to honor the past, make peace with the present, and overcome the trials and tribulations of the future.

From a physical/scientific standpoint.

Fasting has been found to promote health benefits when done in a controlled manner over regulated periods of time. They recently discovered that if an individual fasts for a period of three days, their immune system resets itself.

http://www.telegraph.co.uk/science/2016/03/12/fasting-for-three-days-can-regenerate-entire-immune-system-study/

Your body uses the time without food to correct issues on a biological level.

Keep in mind, these are controlled fasts which are not extended beyond this period of time. Going beyond this period of time can harm you if you withhold sustenance for too long. Our bodies need nutrition to function correctly.

I come from the mindset that no law is strictly physical/spiritual. They blur into one another and provide benefits which merge those aspects.

Fasting is powerful in a spiritual sense because you are choosing to take control of a baser instinct. Hunger is as basic as breathing or sleepiness, so by choosing to overrule that instinct in reflection of a spiritual observance/exercise you are strengthening your divine traits and suppressing primal traits. Torah teaches that the Nefesh HaBehamit "animal soul" is in conflict with our Nefesh Ha'elokit (divine soul)

If you are interested in a more detailed explanation of the parts of the soul, you can read more in the Tanya at this link:

http://www.chabad.org/library/tanya/tanya_cdo/aid/7880/jewish/Chapter-1.htm

These comprise two different sections of our soul which are in a battle for control. By doing spiritual exercises (such as fasting) you can drive down the animalistic urges and raise yourself to a higher state of craving. You can move from craving that which is harmful to craving that which is beneficial if you practice and focus your time/energy. Fasting is just one of those exercises.

Fasting also has a symbolism associated with it in relation to the pain that hunger causes. When we observe Tisha B'Av (just one example) we fast. This holiday is a memorial in reflection various wrongs of Jewish history. One of the main reflections is on the loss of the holy temples (first and second).

Some reading regarding Tisha B'Av and the tradition of the observance:

http://www.chabad.org/library/article_cdo/aid/946703/jewish/What-happened-on-the-Ninth-of-Av.htm

This hunger pain is symbolic of the spiritual pain of our people. We sit in hunger and reflect on this pain and attach that pain to the wrongs and errors of Jewish history. By doing that, we take an impersonal history and we connect to it. I can't know what it was like to lose the holy temple because I never had the holy temple. That doesn't mean I can't reflect on what that loss has done to my ancestors and my peers of today.

By connecting the pain of our people to a pain which is rooted in our biology, we groom ourselves to make the suffering of our past a part of who we are. That strengthens us and drives us to honor the past, make peace with the present, and overcome the trials and tribulations of the future.

A very detailed reading regarding the purpose of fasting in relation to Judaism:

http://www.aish.com/atr/What_is_the_Purpose_of_Fasting.html

From a physical/scientific standpoint.

Fasting has been found to promote health benefits when done in a controlled manner over regulated periods of time. They recently discovered that if an individual fasts for a period of three days, their immune system resets itself.

http://www.telegraph.co.uk/science/2016/03/12/fasting-for-three-days-can-regenerate-entire-immune-system-study/

Your body uses the time without food to correct issues on a biological level.

Keep in mind, these are controlled fasts which are not extended beyond this period of time. Going beyond this period of time can harm you if you withhold sustenance for too long. Our bodies need nutrition to function correctly.