A fast day is not only a sad day, but an opportune day.

Watchman’s notes: Christians need to know that God’s will for salvation includes both Jews and gentiles. This is written in the Bible. Jesus has told us to pray according to God’s will. During the time when the Jews are fasting and mourning what shall we do? I believe each should seek God and pray too for them. Some Christians may fast too. My experience is that fasting and praying as a small group helps one to focus and not be easily discouraged. On the other hand, some watchmen may find it more convenient to fast and pray alone. I pray all of us receive fresh revelation and insight to pray for not just the Jewish people but also for those nations that God has imprinted on our hearts at this time of great strife and fear among the nations of the world.

The fast of the 17th of the Hebrew month of Tammuz, known as Shivah Asar B’Tammuz, is the start of a three-week (July 24 – August 14) mourning period for the destruction of Jerusalem and the two Holy Temples.
The sages explain: “Every generation for which the Temple is not rebuilt, it is as though the Temple was destroyed for that generation.” A fast day is not only a sad day, but an opportune day. It’s a day when we are empowered to fix the cause of that destruction, so that our long exile will be ended and we will find ourselves living in messianic times; may that be very soon.
The fast (abstain from eating or drinking between dawn and nightfall) commemorates five tragic events that occurred on this date:

Moses broke the tablets when he saw the Jewish people worshipping the Golden Calf.
During the Babylonian siege of Jerusalem, the Jews were forced to cease offering the daily sacrifices due to the lack of sheep.
Apostomos burned the holy Torah.1
An idol was placed in the Holy Temple.2
The walls of Jerusalem were breached by the Romans, in 69 CE, after a lengthy siege. (Three weeks later, after the Jews put up a valiant struggle, the Romans destroyed the second Holy Temple on the 9th of Av.)
The Jerusalem Talmud maintains that this is also the date when the Babylonians breached the walls of Jerusalem on their way to destroying the first Temple.

Abstaining from food and drink is the external element of a fast day. On a deeper level, a fast day is an auspicious day, a day when G‑d is accessible, waiting for us to repent.

(above quoted from: http://www.chabad.org/library/article_cdo/aid/479885/jewish/The-17th-of-Tammuz.htm)

Also read: http://www.chabad.org/library/article_cdo/aid/144558/jewish/Tisha-BAv-and-the-3-Weeks.htm