Like u/MrMcGasion said, zeroing makes it easier to recover original data. Data storage and signal processing is pretty much a game of threshold values. From digital world you might see 0 or 1, but in reality it's a charge on a certain scale, lets assume 0 to 100%. Anything above 60% would be considered 1 and anything below 45% a 0. Or something like that.

When you do zero the drive, that means drive will reduce charge enough to pass the lower limit, but it will not be 0 on any account. With custom firmware or special tools it is possible to configure this threshold and all of the sudden it is as if your data was never removed. Add to this situation existence of checksums and total removal of data becomes a real challenge. Hence why all these tools do more than one operation to make sure data is really zeroed or removed.

For this reason random data is better approach is much better than zeroing because random data alters each block differently instead of just reducing charge by a fixed amount, as it is with zeroing. Additional safety is achieved by multiple random data writes.

All of this plays a role only on magnetic storage, that is to say HDDs. SSD is a completely different beast and wiping SSD can lead to reduced lifespan of the drive without actually achieving the desired result. SSDs have write distribution algorithms which make sure each of the blocks are equally used. So while your computer thinks it's writing something at the beginning of the drive, in reality that block can be anywhere on the device and address is just internally translated to real one.