You would be happy with any of three people leading an association, but strongly oppose a fourth. A single-choice ballot makes you choose among your acceptable candidates. Approval voting lets you mark all three. Each approval counts once, and the candidate with the largest total wins.
This changes what a ballot can communicate. Supporting a compromise no longer requires withholding support from your favorite. The basic approval-voting procedure is easy to count because every candidate's total is simply the number of voters who approved them. It does not require transferring ballots between rounds.
Where to draw the line
The ballot leaves the meaning of “acceptable” to the voter. Someone may approve everyone they could tolerate; someone else may support only their first choice to avoid helping a competitor. The resulting totals therefore measure approvals under a particular strategic situation, not a neutral psychological quantity.
For a committee choosing a guest speaker, members could approve everyone they would be willing to invite and then check the leading candidate's availability. That is different from rating how strongly they prefer each person or ranking the entire list. Approval ballots also need clear rules for ties and invalid marks. The method opens up one kind of expression while deliberately leaving differences among a voter's approved candidates unrecorded.