After a person has received the Holy Ghost and been baptized by fire, the Holy Ghost inspires them with the ability and the vocabulary to “speak with the tongue of angels” so that they might “shout praises unto the Holy One of Israel” (2 Nephi 31:13). Speaking with the tongue of angels does not necessarily mean that a person would speak in another language.
President Boyd K. Packer explained that we speak with the tongue of angels when we speak by the influence of the Holy Ghost: “Nephi explained that angels speak by the power of the Holy Ghost, and you can speak with the tongue of angels, which simply means that you can speak with the power of the Holy Ghost. It will be quiet. It will be invisible. There will not be a dove. There will not be cloven tongues of fire. But the power will be there” (“The Gift of the Holy Ghost: What Every Member Should Know,” Ensign, Aug. 2006, 49–50).