There are a few uses for dripstone, so let's take a look at them below.

With the pointed dripstone that you grow, you will be able to craft dripstone blocks. To do so, you will need four pointed dripstones, which can see been in the image above.

infinite lava source created with dripstone

With a stalactite and cauldron, you can make an infinite water or lava source. To do this, set up a cauldron with a dripstone block at least two blocks above, as seen in the image above. Under the dripstone block, place a pointed dripstone.

Finally, you will need your liquid of choice in the space above the dripstone block. For this example, we used lava. With lava above the dripstone block, the stalactite will slowly drip it into the cauldron, filling it up. After about one in-game day, the cauldron will be filled with lava, while the lava above the dripstone block will remain the same. This is helpful if you have set up your base in an area where there isn't much lava.