But the main way to merit Olam Haba is by guarding one's tongue. That is worth more than all the Torah and good deeds. This is the meaning of (Isaiah 32:9) "tranquil women" (Berachos 17a) because the mouth is the holiest of the holy.
How does “tranquil women” relate to the mouth being holy?
The point the Vilna Gaon is trying to emphasize is guarding one's tongue, Rav Dovid Altschuler in his Metzudos Zion and Rav Meir Leibush Wisser - the Malbi"m, both comment on that verse explaining the term "שאנן" to connote tranquility that comes from silence. Therefore this verse is quite apropos in buttressing the notion of watching one's speech, or remaining quiet and refraining from speaking vainly.