The Rebbe explains the significance of the Seventeenth of Tammuz, and the lesson to be derived from it.
On 17 Tammuz, the walls of the city of Yerushalayim were breached.

The purpose of a wall is not to isolate oneself from the outside world, for a proper wall has gates in order to enter and leave. Rather, a wall exists to protect against the penetration of undesirable influences.

[In the case of the walls of Yerushalayim,] however, [by departing from the city through the gates in the wall,] the wall had a constructive impact upon all matters outside the wall, and upon the entire outside world.

Thus, as long as the wall of Yerushalayim was intact, this represented the completeness of the state of the Jewish people. They were both protected from undesirable outside influences, and able to rectify and perfect the outside world by exiting from the wall’s gates.

Thus, the breaching of the walls symbolizes a lack of protection from undesirable influences. Thus, when the walls were breached, the non-Jews invaded Yerushalayim. An undesirable relationship between Jews and non-Jews was then formed.

We rectify this by establishing a desirable relationship between Jews and non-Jews—through Jews influencing non-Jews to abide by the Noahide Code. Thus, 17 Tammuz is an auspicious time to intensify our efforts in influencing non-Jews, and so it is also an appropriate occasion to mention yet again the need to influence non-Jews to adhere to the Noahide Code.

Hisva’aduyos 5744, Vol. 4, p. 2251.
In my own words: The seventeenth of Tammuz represents the sin of having some degree of inappropriate contact with non-Jews and their culture, and in our generation we still suffer from this malaise. We have sinned by imbibing secular influences that should have been utterly foreign to us (see here), and thereby compromising our unique role (see here).