There are very few things that are as critical when fishing than the piece that connects you to the fish. That piece is the line but the knot used is what keeps that jig connected to your line. If your knot is weak or not the right knot for the job, your chances of loosing that fish grow exponentially.
There are a lot of knots out there but hands down the best and strongest knot for tying on a jig is the palomar knot.
The palomar knot is consistently strong and in our opinion the single best knot for tying on jigs. The knot works great with braid and flourocarbon and here is a great link to how to tie the knot if you are not already familiar with it:
But why this knot over any other? It is incredibly strong! After I tie the knot on the jig, I test the knot by pulling the line against my knee to test. If it is going to break or slip, this is when it is going to happen.
While I am sure there are other great knots out there, I have found that this is simply the best knot for fishing with a jig!