The terms "Old Testament" and "New Testament" are traditionally used to refer to the two major parts of the Bible. The "Old Testament" is taken to be that part of the Bible which was written before the life of Jesus on the earth. The "New Testament" is taken to be what was written afterwards.
This usage of these terms is very old and well-established. From the historical evidence that we have, it appears that "Irenaeus was the first to apply the term N.T. [New Testament] to sacred scriptures and that after his times the description of them as the 'New Testament'...came into vogue." (W. C. van Unnik, "E kaine diatheke - A Problem in the Early History of the Canon," Studia Patristica, vol. 4, p. 214.) 
It seems that Melito of Sardis is to be credited "for the first use of the term Old Covenant or Old Testament to refer to the Bible." (S. George, ed., Melito of Sardis, p. xxx.) Irenaeus and Melito wrote between A.D. 160 and 190 - eighteen hundred years ago, but more than a century removed from the events described in the Gospels.
The traditional use of these terms, then, is quite old, but it is still very incorrect.  "Old Testament" and "New Testament" actually refer to the two major covenants which the Lord made with Israel - the "old" covenant of the Law and the "new" covenant in the blood of Yeshua.  The proper Biblical terms are "Old Covenant" and "New Covenant." 
These covenants are particular agreements, not designations for the two major parts of the Bible. For example, when Paul speaks of the Old Covenant as having faded away, he is speaking of the Covenant of the Law, not of the Scriptures themselves. (cf. 2 Co. 3)  The Scriptures, and the Law of God which they contain, are eternal. It is only the covenant that has faded away.
The traditional labeling leads to the erroneous belief that the "Old Testament" was for the Jews, and the "New Testament" is for the Church. It leads to the erroneous belief that the "New Testament" is to be interpreted differently than the "Old Testament." The traditional labeling also leads to the erroneous belief that "the God of the Old Testament" is a God of wrath, and "the God of the New Testament" is a God of mercy. This error is compounded by ignoring both God's love for Israel and God's promises of judgment in the Church, and of wrath and judgment in the world. These are fundamental errors. God is One. He and His purpose are unchanging. He presents the gospel as the fulfillment of what He planned and promised from the beginning. The plan, the promise, and the fulfillment are inseparable.
Yeshua referred to "the Law of Moses [Torah] and the Prophets [Nevi'im] and the Psalms [Ketuvim]." (Lk. 24:44)  The acronym for these parts of the Bible is TaNaKh. In our discussion, the term "Tanakh" will be used.  Inasmuch as there is no current acronym for the Gospels, Acts, the Epistles, and Revelation, the term "New Covenant Scriptures" will be used to encompass them.