Simply put, virtualisation isn't the answer to everything, but it is great!
You say add another layer/makes it run slow, but, in modern systems, this is not actually that much. Many techniques and features exist now that make this "layer" minimal (Such as Intel VT-x, AMD-V). If you are using hypervisor based virtualisation, this layer is even smaller still.
However, based on the way that disks and memory are utilised, it is possible to see speed increases in some situations.
Now, a quick summary of virtualisation products as there is some confusion. There are 4 categories, with most being quite different:
Hypervisor - The smallest overhead and usually rock solid, designed for 24x7 virtualisation. (E.g. Microsoft Hyper V, VMware ESXi.
Desktop (software based) Virtualisation - Generally designed for programmers, testers and IT pros - Speed is still very fast/near native on modern machines, but, at the mercy of the guest operating system it runs under, so, whilst I am running 3 VMs 24x7 on my machine for various tasks, it isn't really "designed" for this - (e.g. Microsoft Virtual PC, VMware Workstation, Sun (Oracle?) Virtual Box). These emulate an entire virtual computer.
Server (software based) Virtualisation - this was quite a large market for a while, but, it was less capable than Hypervisor and is generally a dead market now. Basically it is desktop virtualisation that is just optomised for a server environment - (e.g. Microsoft Virtual Server, VMware Server.
Software Virtualisation - As per comments, I left this one out. This is a specialised market which is usually for virtualising single programs (e.g. Microsoft App-V, VMware ThinApp). This creates a thin "layer" between your computer and the software - it basically intercepts all calls made by the program in order to redirect file/registry writes and basically sandbox the application. This has a few benefits such as the ability to run multiple versions of some complicated applications and makes deployment quite easy (all though, it can be a difficult area to understand/get in to).
As for why they are so popular now - It all comes down to cost and administration time.
For example, in my company, I need to run many "systems" for various systems I use... SQL Server, an intranet system, billing system, email system, VOIP, a legacy system for some old software I have for a few clients and a few more - granted that some of these can be run from the same box, but, for a long list of boring reasons, I want to split them up.
This choice in 2004/5 meant that I had 6 servers here that were on 24x7 - it worked great, but, each machine had 2GB of memory (when it was expensive!), and a P4 era processor that I could cook an egg on. The processors on all the systems hardly went above 5%... maybe a peak at 10-15%, but the majority idled on 0% for almost the life of the machines.
In electricity, I really can't remember, but, I believe this cost me around £100 per machine per year.
Now, if I had instead virtualised this environment (which I ended up doing), I was able to move all of these systems to a single machine and benefit from many features such as oversubscribing memory.
What this means is, my 6 machines each had 2GB of memory, but, on average they were all using around 1/4 of that - On this new machine, I was able to just put in 8GB, and, in a seamless P2V (Physical to Virtual - the process of migrating a machine) move, I have all my machines running as fast as they ever were... in fact, they are faster (as it has a faster CPU).
In addition to this, there are many other benefits such as migration (V-Motion) and high availability that just make virtualisation a brilliant choice.
It should also be said that there are some extras that many home/non business users do not think about - I was able to get rid of some of my networking equipment, loose a load of cables, no need for my expensive KVM... I could drop 5 UPSs and my PDU... And best of all, it fits in a single cupboard/out the way instead of the annoying huge humming of a ventilated rack! ... and not such an important need to run air conditioning so high in the summer (which I didn't factor in to the electricity costs above).
I may have been small, but, think of larger companies doing this on a larger scale - I once helped a largeish company migrate over to a virtualised environment - They didn't have the budget, so, I negotiated that my contract terms were that I would get any cost savings for 1 year, and 20% for the next 3... It paid me very well, and, they enjoyed the administration benefits in the first year - and huge cost savings going forward.
I hope this answers your question! If you have follow up questions, I will be happy to answer them.