What are modern day prophets?
The Lord communicates with us his children in different ways. He will speak to us personally, through the Holy Ghost, for matters that are personal, or pertaining to those within the sphere of our influence. When He wants to give a message to the world though, He uses prophets. Christians, Jewish people and Muslims all accept prophets of the Old Testament such as Noah, Jonah and Moses. However, we begin to part ways after that.
As members of The Church of Jesus Christ of Latter-day Saints, we believe that after a long period where God did not send prophets to the people (a time of apostasy), He began to speak to man again with Joseph Smith. After Joseph was martyred, the Lord chose Brigham Young. We have had a prophet on the earth since that time. Our current prophet is President Russell M. Nelson. We call him, “president” because he is the head of the church temporally as well as spiritually. You can read many of his messages to us here.
To differentiate the prophets of the Old Testament from the prophets of our time, we use the term “modern-day prophets” to mean Joseph Smith and all the other prophets though President Russel M. Nelson.
Thanks for asking Catalino!