Even though today is not, technically speaking, a day of obligatory fasting for Catholics (the "meatless" part is obligatory), the readings for Mass are all about fasting. But what God considers fasting, and what we construe it to be turn out to be pretty different concepts. The Gospel is rather sparing: we just see some people from John the Baptist's "school" wonder out loud why Jesus' disciples are (to say the least) not noteworthy for their ascetical practices. Jesus says, in effect, "Oh, they will be someday. Just not today." Not while he, the Bridegroom, is with them.
So we have a context for fasting, and it has to do with the presence or absence of Jesus as Bridegroom.
Isaiah, on the other hand, imagines God calling for a real fast, and he wants it, well, fast. Not fasting in the sense of starving yourself in a feet of asceticism for its own sake, but a form of self-deprivation that lets you really feel the pain of those who have no option but to fast every day: the desperately poor, those who are in chains or oppressed or homeless. And God says this kind of fasting can't happen too soon: "Would that today [there's that word again] you might fast so as to make your voice heard on high!"
What's the connection? It's Jesus again (as always!). He assures us that when we practice those works of mercy, when we "release those bound unjustly, untie the yoke, set the oppressed free, share bread with the hungry and clothe the naked and shelter the homeless, "you did it for me."