The first siege of Jerusalem ended with the breaching of the walls on this date. We fast on the 17th as this was the day the walls were breached at the time of the destruction of the second Beis Hamikdash.
Explaining one of the Slichos we say on 17 TAMUZ.
Some thoughts (5774/ 2014).
The upsides of the fasts, and specifically of Shiva Asar BiTamuz
Fast Days: An overview (5777/ 2017)
An overview of the Rebbe’s thoughts on Fasts as days for Teshuva and opportunity. When Moshiach comes they will be transformed to holidays, why? We also discussed specifically the event of the walls of Yerushalayim being breached.
17 Tamuz כיון דאידחי אידחי
The Rebbe’s idea that there cannot be any contradictions in G-d’s Truth, so if Shabbos doesn’t let us fast, Hashem is saying don’t fast today, therefore רבי holds we shouldn’t fast at all.