Let me recommend you first to read [this Q/A][1]. It is about rotations and can hint to or partly answer your question.

A more specific answer from me about interpretation might be as follows. Theoretically, factor of Factor analysis is a univariate latent feature, or essence. It is not the same thing as a set or cluster of phenomena. Term "construct" in psychometry is generic and could be conceptualized as factor (essence) or cluster (prototype) or something else. Since factor is univariate essence it should be interpreted as the (relatively simple) meaning lying on (or "behind") the *intersection* of the meanings/contents of the variables loaded by the factor.

With oblique rotation, factors are not orthogonal; still, we usually prefer to interpret a factor as clean entity from the other factors. That is, ideally, factor X *label* would dissociate from a correlated factor Y label, to stress individuality of both factors, while assuming that "in reality" they correlate. Correlatedness gets to be isolated characteristic of entities from labels of the entities.

If it is this the strategy typically preferred then **pattern** matrix appears to be the main tool for interpretation. Coefficients of pattern matrix are the *unique* loads or investments of the given factor into variables. Because it is regression coefficients. **Structure** matrix contains (zero-order) correlations between factors and variables. The more two factors X and Y correlate with each other the greater *can* be the discrepancy between the pattern loadings and the structure loadings on some variable V. While V ought to correlate higher and higher with both factors, the regression coefficients can rise both *or* only one of the two. The latter case will mean that it is that part of X which is different from Y what loads V; and thence the V-X pattern coefficient is what is highly valuable in interpretation of X.

Weak side of pattern matrix is that it is less stable from sample to sample (as usually regression coefficients in comparison to correlation coefficients). Relying on pattern matrix in interpretation requires well planned study with sufficient sample size. For pilot study and tentative interpretation structure matrix might be better choice.

Structure matrix seems to me potentially better than pattern matrix in back interpretation of *variables* by factors, if such a task arises. And it can rise when we validate items in questionnaire construction, - that is, decide which variables to select and which to drop in the scale being created. Just remember that in psychometry common validity coefficient is correlation (and not regression) coefficient between construct/criterion and item. Usually I include an item in a scale this way: (1) look at maximal correlation (structure matrix) in the item's row; (2) if the value is above a threshold (say, .40), select the item *if* its situation in pattern matrix confirms the decision (i.e. the item is loaded by the factor - and desirably only by this one - which scale we're constructing).

If you do not perceive a construct as univariate trait using classic factor analysis would be questionned. Factor is thin and sleek, it is not like pangolin or armful of whatever. Variable loaded by it is its mask: factor in it shows through what appears to be completely *not* that factor in it.

  [1]: http://stats.stackexchange.com/q/151653/3277