In addition to the launch being a risky thing in and of itself – we're carrying a very delicate instrument into space by shooting it into orbit on a rocket, after all – what is especially fraught is what comes after it makes it into low Earth orbit.
From there, it has to propel itself out to a distance of 1 million miles (1.5 million kilometers), making a number of maneuvers to position itself at its L2 destination. A misfired thruster or some other mistake could knock it off course so that it doesn't reach the stable L2 orbit it needs in order to complete its mission.
It's also travelling far beyond the moon, somewhere that humans have never gone in person. So, if something breaks along the way, there's no way for us to go up there and fix it the way we did when we discovered Hubble's mirror had a key flaw that was screwing up images.
Astronauts were able to go up and fix Hubble's mirror so that it was able to operate as planned. We can't do the same for the James Webb Space Telescope.
What's more, there are hundreds of points of failure that could render the James Webb Space Telescope useless. We need to succeed at each one of those points, or else this was all for nothing. Worse still, much of this involves maneuvers and operations that we've never attempted before, so we have to get everything right on the first attempt.
Needless to say, it's going to be a tense month all around.