Many PDFs are distributed as encrypted PDFs to lock out some of their functionality (eg printing, writing, copying). However, PDF cracking software is available online, which usually cracks the PDF passwords in less than 1 second. 

It doesn't make sense that the PDF system is so easy to crack if Adobe implemented a proper encryption techniques in their document security, and it looks like that there is some major implementation error in their PDF encryption scheme that allows documents to be unlocked with trivial amounts of work. 

What is the security scheme used in such locked PDF files, and why do these PDF password removers take so little time to defeat it? 

There are two types of PDF protection: Password-based encryption and User-Interface restrictions. You are describing the second type of protection, namely the missing permission to copy-and-paste, to print and so on. If there are user-interface restrictions placed on a PDF file, the viewer still needs to decrypt the contents to display it on your screen, so you are not in an "password-based encryption" scenario where you are missing a key to decrypt the document, but in a "DRM" scenario where you trust that the applications that are able to decrypt the file (based on static knowledge like master keys) do only the things the author wants them to do.

Nothing prevents computer experts reverse engineering how the legitimate application decrypts the data (no password needed), and performing the decryption themselves. After having the document decrypted, rights may be "adjusted" to e.g. include printing permission or the decrypting application can do things (like copy all bitmap images) itself.

Adobe tries to prevent "rogue applications" that allow you to circumvent the usage restrictions by their license on the PDF specification: They revoke the license to use the (claimed) intellectual property in that specification for applications that do not obey the usage restrictions. AFAIK some open source tools have or had a build switch for whether the usage restrictions should be obeyed or not. This makes a perfect starting point for people selling "PDF deprotector" software.

In the case described above, the "user password" is the empty string. PDF readers are required to try to an empty user password if a protected PDF file is opened. Only if that fails the password validity check is the user asked for a password. begueradj describes the key derivation in his answer, and as you see, the "DRM permissions" (/P entry) enters the key derivation, so if you just "fix the permissions" in a protected PDF file, a conformant reader will derive the wrong key and fail to open the document. On the other hand, if a PDF file is completely protected by a password (even against opening), the user password is no longer empty, and this type of PDF protection is reasonably secure.
