People's Dictionary of the Bible 
Degrees, Songs of. Fifteen Psalms 120:1-7; Psalms 121:1-8; Psalms 122:1-9; Psalms 123:1-4; Psalms 124:1-8; Psalms 125:1-5; Psalms 126:1-6; Psalms 127:1-5; Psalms 128:1-6; Psalms 129:1-8; Psalms 130:1-8; Psalms 131:1-3; Psalms 132:1-18; Psalms 133:1-3; Psalms 134:1-3, are so entitled. A variety of reasons has been suggested to account for this. The Jews believe that they were sung by the Levites on the fifteen steps which separated the men's court from the women's in the temple. Gesenius suggested that there was a progression in the thought and phraseology: the last member of a verse or part of it being taken up, repeated, and amplified in the next verse, thus:
"I will lift up mine eyes unto the hills,
From whence cometh My Help.
My Help cometh from the Lord,
Which made heaven and earth."
— Psalms 121:1-2 .
Watson's Biblical & Theological Dictionary 
Psalms of Degrees is a name given, to fifteen psalms, from the 120, to the 134, inclusive. The Hebrew text calls them a song of ascents. Junius and Tremellius translate the Hebrew a song of excellences, or an excellent song, from the excellent matter they contain. Some call them psalms of elevation, because they were sung with an exalted voice, or because at every psalm the voice was raised; but the translation of psalms of degrees has more generally obtained. Some think that they were called psalms of degrees, because they were sung upon the fifteen steps of the temple; but they are not agreed where these steps were. Others are of opinion, that they were so denominated, because sung in a gallery, which was in the court of Israel, where the Levites sometimes read the law. Calmet thinks, that they were called songs of degrees, or of ascent, because they were composed on occasion of the deliverance of the Jews from the captivity of Babylon, either to implore this deliverance from God, or to return thanks for it after it had been obtained; and that the Hebrews used the term to go up, when they spoke of their journeying from Babylon to Jerusalem. Others are of opinion, that these psalms were sung during the time of service, while the flesh, &c, were consuming on the altar, and while the fume and smoke ascended toward heaven; and that the title Psalms of Ascent seems to favour this supposition. The point is involved in entire obscurity; and, after all, the title of these Psalms may be only a musical direction to the temple choir.
Cyclopedia of Biblical, Theological and Ecclesiastical Literature 
(French degre, from Lat. gradus, a step), titles of rank to which are annexed privileges, conferred upon students in colleges and universities, or upon members thereof, as a testimony of their proficiency in the arts and sciences. The term "Arts," or "Liberal Arts," as technically applied to certain studies, came into use during the Middle Ages, and on the establishment of universities, the term "Faculty of Arts" denoted those who devoted themselves to science and philosophy as distinguished from the faculty of theology, and afterwards of medicine and law. The number of" ‘ arts" embraced in the full mediaeval course of learning was seven: Grammar, Logic, Rhetoric (constituting the Trivium), Music, Arithmetic, Geometry, and Rhetoric (the Quadrivium). The terms master and doctor were originally applied synonymously to any person engaged in teaching. In process of time, the one was restricted to the liberal arts, the other to divinity, law, and medicine. When regulations were established to prevent unqualified persons from teaching, and an initiatory stage of discipline was prescribed, these terms became significant of a certain rank, and of the possession of certain powers, and-were called gradus, "steps" or "degrees." The passing of the initiatory stage, said to have been first instituted by Gregory IX (1227-41), conferred the title of bachelor (q.v.), and an additional course of discipline and examination was necessary to obtaining that of master. The title of Master of Arts originally implied the right, and even the duty of publicly teaching some of the branches included in the faculty of arts; a custom which is still retained, to some extent, in the German universities, but has fallen into disuse in other countries. The degrees of D.D. (doctor divinitatis), S.T.D. (sacrce theologice doctor), and LL.D. (doctor utriusque legum), are conferred, honoris causa, by colleges and universities, upon persons held to be worthy of them, whether members of the said institutions of learning or not. The see of Rome claims a universal academical power, and the Pope confers the doctor's degree at pleasure. See Kirkpatrick, Historically received Conception of the University; Newman, Office and Work of Universities, p. 241; Tholuck, in Herzog's Real-Encyklopadie, 16:722; and the article (See Doctor).