A runt is an unappealing short line at the end of a paragraph. It's usually only one word, but sometimes it's a couple or three really short words.
Runts are sometimes known as widows, but a widow is the first line of a new paragraph at the bottom of a page (an orphan, on the other hand, is the last line of a paragraph at the top of a page). I really hate the term "runt", and I wish whoever coined the term had called them urchins, to preserve the Dickensian tone. The term runt is all over the internet now, so I guess we are stuck with it.
As far as I can tell, Robert Bringhurst doesn't have a name for them at all. In The Elements of Typographic Style, he writes "Avoid leaving the stub-end of a hyphenated word, or any word shorter than four letters, as the last line of a paragraph."
I'm much less lenient than Bringhurst. I prefer the last line of my paragraph to be at least a third of the measure (column width). This sometimes creates spacing issues if you're using justified alignment without hyphenization (which I almost always am). I'd rather have a short last line than ugly spacing.
Manually fixing runts
One way to fix runts is to replace the space between the last two or three words with a non-breaking space (InDesign: Opt+Cmd+X). Another way is to create a character style called "No Break" which has the "No Break" option checked under "Basic Character Formats". Both these methods are tedious, so I prefer to let InDesign do the work for me using GREP styles.
Automatically fixing runts
In the Paragraph Style Options editor, select the GREP Style tab and create a new GREP style.
Next to Apply Style, select your No Break style, or create one. You might want to create a new style based on "No Break" called something like "fix runts", and temporarily set the character color to red. This will show exactly which words are being affected, and you can easily scan the document looking for spacing issues.
Which characters are being affected are determined by the GREP expression you put in the To Text: field. My own expertise in GREP is limited to knowing when it can save me time and being able to hack it enough to suit my needs. I've collected the following GREP expressions from various places on the internet:
My favorite GREP expression for fixing runts
I love this one because of it's simplicity.
This ensures that the last ten characters of a paragraph are never broken. I usually change this value to 15 or 20. Sometimes, I'll create separate paragraph styles with lower values and none at all to use in the event of weird spacing issues.
Other GREP expressions for fixing runts
From a very helpful page on GREP styles. You'll find an in-depth discussion of this expression over there.
I'll add more as I come across them.