Minecraft wiki entry for Skyblock, associated text: Blackstone is an alternative to Cobblestone used to create Brewing Stands, Furnaces, and stone tools. While it isn't usually useful, it is extremely important if the player doesn't have a cobblestone generator.
Crying Obsidian is used to create Respawn Anchors.
Gravel can be used to create Coarse Dirt, which can be tilled into dirt allowing it to be duplicated, or to obtain Flint used to create Arrows, Flint and Steel and Fletching Tables.
Nether Quartz is used to create Daylight Detectors, Observers and Redstone Comparators - useful for automation.
Soul Sand is used to summon the Wither or to create Soul Torches and Soul Campfires, used to repel piglins and hoglins.