Alright, I will endeavor to explain.
ZFS stands for Zettabyte file system, it is a system for storing data to the drive. ZFS is actually a set of combined system, that include file system, partitioning, raid tools, and various other tools all designed to work together as a singular system.
There are other file systems such as NTFS (NT File System, the file system microsoft uses for windowsNT and above) and FAT/FAT16/FAT32 (file allocation table, older file systems from microsoft) and exFAT (a new derivative of FAT from MS designed specifically for USB thumb drives, since NTFS is bad for them and FAT32 is ancient).
File systems reside on partitions, which separate a drive into multiple chunks (which show up as separate drives in windows) or, rarely, combine multiple drives together into one partition (ZFS). Common partitions are MBR (master boot record, old and outdated) and GPT (general partition table, modern, lacks support) and the zfs file system (zfs's method can actually combine drives together at the FS/partition level unlike MBR and GPT).
So you can have a 2TB drive running MBR split into two 1TB partitions... one running NTFS and windows, and another running ext4 and linux.
RAID is a technique to create a "virtual drive" from multiple drives for various purposes (which are then partitioned and then used by the file system).
RAID1 is just storing an identical copy on all drives (write speed is the same as single drive, read speed is number of drives times speed of a single drive). All drives but one can fail and your data remains safe. Space is the size of only one drive (so 2x2TB drives give you 2TB of space only)
RAID0 is splitting the data between all drives (write and read speeds are the speed of a single drive times the number of drives.) if ANY drive fails ALL data is lost. Highly unsafe.
Space is just the sum of the drives (2x2TB gives 4TB of space)
RAID5 is using like raid 0, except 1 drive is reserved to contain the mathematical results of performing a calculation on the data on the other drives, such that you could recover the data if any one drive fails. write and read speeds can in theory go as high as the speed of a single drive times the number of drives minus 1... except in reality the complexity of the process means that only the fastest controllers (300+$ ones) can do that, most perform much slower than a single drive.
Space is the size of all drives but one... so 5x2TB drives will give (5-1)*2TB = 8TB space.
There are some problems with the implementation that can cause dataloss in a variety of conditions (write hole, reconstruction fails due to corrupt sectors, and more), and motherboard implementations are all terrible (slow AND unreliable).
RAID6 is raid5 only with 2 drives each containing a different mathematical result, allowing 2 drives to fail without data loss, and losing the space / speed of 2 drives.
RAID1+0 or 0+1 or 10 or 01 is when you make a RAID1 of a RAID0 array, or vice versa. reliability and speed is a mix of raid0 and raid1. pretty nice but requires lots of drives.
RAIDZ is a special implementation of RAID5 that fixes all the problems that can cause dataloss in RAID5 (except, of course, drive failure... I mean it fixes the write hole, the reconstruction errors, etc). However in order to do so it has to limit you to ZFS file system.
RAIDZ2 is the same thing for RAID6.
ZFS has several huge advantages over older file systems, foremost that it has unmatched data security, it is the only filesystem that prevents data corruption by saving checksums for all your data. As long as you have a redundant storage system (raid1, raidz, raidz2, raid10, or have set it to keep multiple copies of a file via the copies=N command) then it will repair data corruption on the fly.
NTFS and ext4 don't have that...
ZFS is the only file system that does that that is complete and commercially available...
Google has a custom file system (that actually sits on top of ext2, although they have begun work migrating it to ext4) that is their greatest trade secret and not available for sale. It also has robust data safeties.
The company that designed ZFS (Sun, which was purchased by oracle) released it as open source under the CDDL open source license. GPL forbids the use of software of certain license types, and as a result linux cannot implement ZFS as is, only via a userspace module (FUSE), which is how linux implemented NTFS, but this is a slow and long process.
Apple begun implementing ZFS but it seems to not go anywhere, and FreeBSD has ported ZFS (the BSD open source license called BSL permits the use of CDDL type software).
CDDL, GPL, and BSL all are legal licenses that allow the use of open source software under various conditions.
Anyways, due to its incompatibility with license of ZFS source code, and fear of nefarious intents from SUN, linux community began development of their own GPL alternative to ZFS called BTRFS (better file system), which is currently not ready for use. They could have just written ZFS compatible code from scratch instead, but they didn't trust SUN (or whomever buys them) to not later sue them for patent issues.
This turned out to be wise as SUN was purchased by oracle, who immediately discontinued opensolaris (a fork called illumos is now being maintained by companies that came to depend on it) and has sued google for using java (which is open source SUN product, and which SUN gave many guarantees that you couldn't be sued for using even if they wanted to) in their android OS.
So oracle is actively hostile to open source and is being predatory... not a good sign.
despite its uncertain future, ZFS will not magically disappear in a puff of smoke just because companies change hands and policies, you can still download and use, for free, existing implementation and software. and it is still the ONLY resistant to data corruption file system in the history of humanity available to everyone (the first is the google exclusive google FS). So enjoy it until BTRFS is ready.