What does "Tikkun Leil Shabbat" mean?

What does "Tikkun Leil Shabbat" mean?
First, some vocabulary:
l'taken (v) = to repair or heal
tikkun olam (n) = the holy work of repairing the world
Tikkun Leil Shavuot (n) = The name of our havurah is a play on this term, which refers to the annual all-night Torah study session which spiritually "heals" the world on the holiday Shavuot.

Shabbat (n) = Jewish day of rest from sundown Friday to sundown Saturday, when we stop running around trying to accomplish things and make some time to breathe and bless, eat and love.

Tikkun Leil Shabbat is a welcoming, restful, songful community where we glimpse redemption at dusk on a Friday evening, eat things with tofu and noodles in them, learn from each others' thoughts and experiences, and educate ourselves about the good work people are already doing to make our city a gentler and fairer place for everyone who lives here.