The story about Improved Skyblock is that in a big nuclear explosion, the ground shot up into the air and was ripped from the surface of minecraft. and you where on one of those very parts. So now you survive by building your island.
So basicly you gotta use what you have. You can try to get off the island and derp around in survival(suggested not to since the island is like the only way to get resources)but i will warn you, you can die easily out there :/. Also don't jump from the island, you will fall into a instant death fail.
Enjoy!

~Duckgod12