What does LDAP solve?

I've been in touch with LDAP in many projects I've been involved in but, the truth be told, I don't really understand it. I thought it was just a person directory but after I discovered that it can contain any objects in a hierarchical structure.

I installed openldap in my box and I found many tutorials regarding just the installation.

What is LDAP? What are the scenarios where LDAP is the right choice? What are the LDAP concepts I should know for working with it? What are the advantages of LDAP? Is it used just because old applications used it? Is there a good doc anywhere on internet explaining all this questions?

UPDATE: Complementing the answers I found this link which contains a quick start guide for LDAP newbie like me.

Solution

What is LDAP? What are the scenarios where LDAP is the right choice?

At its core, LDAP is a protocol for accessing objects that are suitable for storage in a directory. Whether something is "suitable" is an entirely subjective determination that's left up to implementers, but typically this means collections of many objects that each have infrequently (or never) updated data, where each object has an obvious or canonical way to be looked up:

a phone book (look up by name or by phone number)
titles in a library (look up by title, author, etc.)
tenants in a building (look up by floor, suite, name, etc.)

and so on.

Note that LDAP itself is just a protocol and doesn't provide any actual storage -- in much the same way, HTTP doesn't imply anything about whether you're using Apache, Jetty, Tomcat, Mongrel, et al. as a web server. (One problem with LDAP in general is the confusing reuse of names to mean different things. Wikipedia has a good section on this.)