Providers are a simply a way of extending and customizing the JAX-RS runtime. You can think of them as plugins that (potentially) alter the behavior of the runtime, in order to accomplish a set of (program defined) goals.
Providers are not the same as resources classes, they exist, conceptually, at a level in-between resources classes and the JAX-RS implementation. If it helps, you can think of them in the same light as device drivers (existing between user and kernel space). This is a broad generalization.
There are three classes of providers defined by the current JAX-RS specification. The commonality between them is that all providers must be identified by the @Provider annotation and follow certain rules for constructor declaration. Apart from that, different provider types may have additional annotations, and will implement different interfaces.
Entity Providers
These providers control the mapping of data representations (like XML, JSON, CSV) to their Java object equivalents.
Context Providers
These providers control the context that resources can access via @Context annotations.
Exception Providers
These providers control the mapping of Java exceptions to a JAX-RS Response instance.
Your runtime will come with a number of predefined providers that will be responsible for implementing a base level of functionality (e.g for mapping to and from XML, translating the most common exceptions etc etc). You can also create your own providers as needed.
The JAX-RS specification is a good reference for reading up on these different provider types and what they do (see Chapter 4).