I love resistance bands because they are so small yet effective, and they can be used with pretty much any type of exercise to intensify it. They're also really great for travel if you want to be able to work out on the go, since they are so compact. Here is an example of a great way to use it for core work:
Amp up standard bicycle crunches by using a resistance band! Loop it around the arches of your feet and lay down on your back. Curl your head, neck, and shoulders off the ground and press your lower back into the ground to engage your core and lift your legs up at a 45 degree angle.
Bring your hands behind your head to support your neck. Draw one knee in towards your chest and twist your upper body towards your leg for an oblique twist. Then hold the twist and use your lower core muscles to tuck your hips up, moving the whole shape of the lower body up. Switch sides, then take alternating bicycle crunches, pushing through the resistance band.