Exploratory factor analysis is the most common technique of factor analysis. It carries the name "exploratory" due to its ability to take in a set of unanalyzed data and give as output the relationships between the variables of the data. This technique essentially allows a researcher to reduce a large set of uninterpretable data to a small set of factors that describe the correlations of the variables in the data.
The word "confirmatory" in the name of this factor analysis technique hints at the technique's purpose: to confirm hypotheses a researcher has about a set of data. Using this technique, a researcher can collect a set of data related to her hypotheses, input the data, and "confirm" whether the data matches her hypotheses in terms of how the data simplifies and the relationships between the variables of interest in the data.
Factor rotation is a technique that allows the user of factor analysis to reorient a set of factors. This technique contains two sub-techniques: orthogonal factor rotation and oblique factor rotation. Orthogonal rotation preserves the orthogonality of the factors, leaving them uncorrelated. Oblique rotation, on the other hand, allows correlation between the factors in the solution. The researcher can choose the form of rotation that suits his purpose.
Interpretation is an important technique in factor analysis, as it allows the user of factor analysis to understand the solution in ordinary language. Factor analysis's close cousin, principal components analysis, does not allow such a technique. This technique is one of the main advantages of factor analysis because it can give the researcher the ability to concisely describe relationships among the variables in the data using the factor loadings output of factor analysis.