This will be very brief and to the point.
Orphans are stranded bits of copy, a single word occupying its own line, such as the word type, above, at the top of the right column. Widows are longer bits of copy, a few words perhaps, occupying a single line that’s become estranged from its native text column, pushed to the top of the next column, alone.
Left unresolved, the presence of widows and orphans reveals to the reader the inattention of the typographer. They throw off the margins; they call undue attention.
In InDesign you can specify a minimum number of lines allowed to break between columns. To do it, apply a paragraph style to the paragraphs you’re working with and set the number of lines in the Keep Options page of that paragraph style’s dialog.
Note that the default Keep with Next value, 0, is probably best to keep at 0 until you know what you’re doing with it.
There. The two lines jumped over to clothe, feed, house, and otherwise eliminate the orphaned status of this previously lost word, type. Solved, right? No. What we’ve covered here is really just one aspect of the craft. The art of typography is creating the kind of flexible compositions that absorb the shocks—both of the problems, as well as those created by their solutions.
Look at the hole left behind in the left column created by our keep options. To fill it, we may have to bump something from a previous page, arbitrarily resize the text frame (and perhaps its surrounding text frames), try something funny with the leading or tracking, italicize some foreign words, or otherwise do some good old-fashioned copyfitting. Or, as I often do when setting longer works, most or all of these. A good layout will permit this kind of editing.