Before Java, programmers had to create separate versions of their programs for each system they were targeting. You might have noticed this if you've ever had to pick your operating system out of a list when installing new software. This can be a pretty big headache from a programmer's perspective, since different computers can behave very differently! Just ask a web developer how much fun it is to write websites that work in both firefox and Internet Explorer!
Java became popular in the early-mid 1990s because of its "write once, run anywhere" mantra. Java is cross-platform, which means that programmers only have to write one version of their program, and it will run on any computer that has Java. That might not sound very impressive to us 20 years later, but back then that was a huge leap forward!
A programmer could write a Java program and then package it up in one of the following ways:
This is where things start to confuse people. Programming languages can be very powerful, and malicious programs can do things like delete or copy your hard drive, or install viruses or keyloggers. This makes it important for the end user to understand what's going on- this is why most people know not to run executable files attached to shady emails!
However, you have very little control over what happens on the internet- one wrong click could send you to a malicious website. Html by itself can't do much, but Java can be embedded in that html in the form of an applet.
That's why all Java applets (and webstarts) are sandboxed. This is just another way of saying that Java limits what an applet can do- applets can't access your hard drive or connect to other servers, for example. That way, even if you do stumble onto a malicious website, that website can't use Java against you.
Or so we thought.
By default, applets and webstarts are not allowed to access things like the hard drive. However, there are many valid reasons for an applet to need to work "outside the sandbox"- you might want an applet to save or load a file, or you might want your game to use your graphics card to run faster.
A programmer can ask a user for extended permissions by signing the applet. This causes the applet to show a dialog to the user asking for permission to run outside the sandbox. The user can still say no, so they are still in control. An applet running outside the sandbox is called a privileged applet, since the user has to grant privileges to access system resources.
This actually worked pretty well for quite a long time. In fact, one of the reasons the next section was such big news was because of how good Java's security was, especially compared to languages like flash.
Then during the spring of 2012, an exploit was found that gave malicious programmers (the media might hype them up as "hackers") the ability to run privileged applets without first prompting the user for permission.
This was a big deal, because any website could do things like modify the hard drive or lock down the system, and the user would not have a good way to track down the cause (compared to the security prompt that should have displayed). Even advertisements could contain a malicious applet, making it even more difficult. Several viruses spread through this applet exploit- one popular virus locked down the user's system and displayed a scary-looking warning from the FBI telling users to enter their credit card information to get rid of the warning. The message wasn't actually from the FBI, and entering your credit card information did not get rid of the message, it only gave thiefs access to your credit card.
This exploit was bad news. However, many people who didn't understand the exploit reacted by declaring Java as a whole insecure, which simply isn't true. This exploit was bad because Java can be embedded in a website, and websites make it hard to be sure where code is coming from (picture a website with 4 advertisements all running code from different places).
However, only a few Java applications are deployed as applets (stuff like code examples, academic stuff, and games work well as applets). Most applications are deployed either as runnable jars (mentioned above) or as packaged executables (mentioned later), and this exploit did not make those applications any less secure. Similarly, a lot of Java code is run on servers (including this website!), and this exploit did not affect that code at all.
So, yes, the exploit was bad. But it doesn't mean that Java itself is insecure, just that applets can be abused to do bad things.
After these exploits were made public, Oracle released a patch fixing the problem. But as soon as Oracle could fix one problem, malicious programmers would find another exploit, starting a back-and-forth that continued for almost two years.
Over the course of those 2 years, Oracle has made significant changes to how applets and webstarts work. For example, Java now prompts the user when ANY applet is run, including applets that are completely sandboxed, and other settings can completely disable Java in internet browsers if the user so chooses.
These changes have thwarted most of the malicious uses of applets, but they've also added a bunch of annoying and scary warnings to perfectly innocent applets.
In January of 2014, Oracle released update 51 for Java, which contained another major change to how Java works on the internet. As of this update, by default, applets will only work if the programmer has paid for a certificate. These certificates can be pretty expensive and can be revoked if they are abused. This makes it even harder for malicious programmers to abuse Java, but it also makes it almost impossible for novices and students to deploy their programs as applets.
The rest of the deployment tutorial contains other options for deploying Java (and Processing).