Servers are the physical infrastructure to run all the layers of software so your web application can respond to requests from clients such as web browsers.
Your web application must live somewhere other than your own desktop or laptop. Servers should ideally be accessible 24 hours a day, 7 days a week, with no unplanned downtime. The servers that host your web application for actual users (as opposed to test users) are known as production servers. Production servers hold real data (again as opposed to test data) and must be secure against unauthorized access.
Understand the difference between bare metal servers, virtual private servers (VPS) and infrastructure-as-a-service.
Sign up for a hosting provider. I recommend getting a Linode VPS to set up your initial infrastructure and deploy your web application there. Digital Ocean and prgrmr are other VPS options. You can change hosting providers later after learning how to deploy web apps.
Provision your first server and move on to the operating systems section.
The term bare metal refers to purchasing the actual hardware and hooking it up to the Internet either through a business-class internet service provider (ISP) or co-locating the server with other servers. A "business-class" ISP is necessary because most residential Internet service agreements explicitly prohibit running web servers on their networks. You may be able to get away with low traffic volume but if your site serves a lot of traffic it will alert an ISP's filters.
The bare metal option offers the most control over the server configuration, usually has the highest performance for the price, but also is the most expensive upfront option and the highest ongoing maintenance. With bare metal servers the ongoing operating cost is the electricity the server(s) use as well as handling repairs when server components malfunction. You're taking on manual labor working with hardware as well as the rest of the software stack.
Buy actual hardware from a vendor either pre-built or as a collection of components that you assemble yourself. You can also buy pre-configured servers from Dell or HP. Those servers tend to be in smaller case form factors (called "blades") but are correspondingly more expensive than putting off-the-shelf components together yourself in a standard computer case.
Virtual private servers (VPSs) are slices of hardware on top of a larger bare metal server. Virtualization software such as Xen and VMWare allow providers such as Linode and prgmr (as well as a many others) to provide fractions of a full server that appear as their own instances. For example, a server with an 8-core Xeon processor and 16 gigabytes of memory can be sliced into 8 pieces with the equivalent of 1-core and 2 gigabytes of memory.
The primary disadvantage of virtualized servers is that there is resource overhead in the virtualization process. In addition, physical constraints such as heavy I/O operations by a single virtualized instance on persistent storage can cause performance bottlenecks for other virtualized instances on the shared server. Choosing virtualized server hosting should be based on your needs for urgency of service ticket requests and the frequency you require for ongoing maintenance such as persistent storage backups.
Choosing a low cost VPS reviews the factors that you should weigh when deciding on hosting providers.
This post covers hosting types and host to choose a web host.
How to set up your Linode for maximum awesomeness shows how to work with a VPS once you've got the server up and running.
Infrastructure-as-a-service (IaaS) overlaps with virtualized servers because the resources are often presented in the same way. The difference between virtualized servers and IaaS is the granularity of the billing cycle. IaaS generally encourages a finer granularity based on minutes or hours of server usage instead of on monthly billing cycles.
IaaS can be used in combination with virtualized servers to provide dynamic upscaling for heavy traffic. When traffic is low then virtualized servers can solely be used. This combination of resources reduces cost at the expense of greater complexity in the dynamically scaled infrastructure.
The disadvantage to IaaS platforms is the lock-in if you have to write custom code to deploy, dynamically scale, and generally understand your infrastructure. Every platform has its quirks. For example, Amazon's standard Elastic Block Store storage infrastructure has at least an order of magnitude worse I/O throughput than working with your local disk. Your application's database queries may work great locally but then when you deploy the performance is inadequate. Amazon has higher throughput EBS instances but you will pay correspondingly more for them. EBS throughput is just one of many quirks you need to understand before committing to an IaaS platform.