In Holacracy, Tension describes a person’s felt sense that there is a gap between the current reality and a potential future.
Although the word 'tension' may have a negative connotation in common usage, Holacracy's use of the term is neutral: The tension itself is the raw felt sense of dissonance, before we label it as "negative" or "positive".
An example of tension might be that your company has published a book, the sales are slow, and you'd like them to be higher. Another might be that a big client has expressed interest in your services, and you already have too many clients than you have time to serve. One might label the first example as a problem, while the second may be seen primarily as an opportunity. As far as Holacracy is concerned, both are "tensions" and require some action to be addressed.
One way Holacracy makes a clear distinction between people and role is by providing processes that help distinguish "personal tensions" (personal preferences, ego) from "organizational tensions" (coming from roles), and not letting the former impact the organization. A good example of this feature is during the Objection round of Governance meetings: one of the criteria used to determine the validity of an Objection is whether the ground for the Objection is limiting one of the objector's roles to do its work. If not, then the objection is deemed not valid.