This verse is dependent on the preceding. So that thou incline. The literal translation is "to incline;" but the inclination of the ear and the application of the heart follow as a consequence upon the precepting ideas (cf.
the Vulgate, ut audiat sapientiam auris tua). The root idea of the original ( קָשַׁב, kashav) is "to sharpen," viz. the ear as expressed, and so to give diligent attention to the precepts of Wisdom. In Proverbs 1:24 it is rendered "to regard."
To apply thine heart is to turn the heart with the whole scope of its powers, in the spirit of humility and eagerness, to understanding. As the ear represents the outward vehicle of communication, so the heart ( לִב, lev) represents the inward, the intellectual faculty, the mind, or it may mean the affections as suggested by the LXX.
καρδία and Vulgate cor. Understanding ( תְּבוּנָה, t'vunah) is here interchanged with "wisdom," which must determine its meaning to some extent. The LXX. interpreters take it as σύνεσις, the faculty of comprehension."
Like בִינָה (vinah) in Proverbs 1:2, the word describes the faculty of distinguishing or separating: but it does not appear to be here used as representing this "as a faculty of the soul, but as a Divine power which communicates itself as the gift of God" (Delitzsch).
A second and perhaps simpler sense may be given to the sentence. It may mean the turning or applying of the heart in an affectionate and loving way, i.e. with full purpose, to the discrimination of what is right and what wrong.
The ideas of wisdom and understanding seem to some extent to be brought forward as personifications. They are things outside of ourselves, to which we have to give attention. Religion appeals not only to the affections, but also to the intellect, as this satisfies all the yearnings of our nature.