What did Edmund Burke mean by "The only thing necessary for the triumph of evil is for good men to do nothing."?

Although this famous quotation has been attributed to the great Irish statesman and political philosopher Edmund Burke, it's by no means certain that he actually said it. However, he did say something that sounds very similar which has a similar meaning:

When bad men combine, the good must associate; else they will fall, one by one, an unpitied sacrifice in a contemptible struggle.

Here, Burke is drawing attention to the natural tendency for the wicked to form themselves into self-serving groups or cabals. It is this capacity for organization that makes evil men so powerfully effective and so difficult to eradicate from public life.
In response to this, the only way that the wicked and their malevolent designs can be defeated is if good men do likewise—by also forming themselves into organized groups. If this doesn't happen, if good men "do nothing," as in the original quotation, then it is certain (as night follows day) that evil will triumph.