@Susan has now provided a solid answer based on the Hebrew usages of the word for "horn," so there is no need no repeat that information. The general picture is that horns symbolize strength and power.
In this answer I will offer some excerpts from the theological writings of Emanuel Swedenborg (1688-1772), covering his symbolic and spiritual interpretation of horns in the Bible, based on that Biblical use as a symbol or metaphor for strength and power.
These are rather old-fashioned translations from the original Latin, but they are the best currently in print for the works I am quoting. Note that "the Word" (Latin Verbum) was the standard Latin term for the Bible, and "the Apocalypse" (Latin: Apocalypsis) was the standard Latin term for the book of Revelation.
In the opening reference for each brief excerpt from Swedenborg's writings, I will provide a link to the original section of Swedenborg's works for those who wish to delve into his full interpretations of horns in the Bible. Swedenborg explains horns in many places in his theological works. The three I am quoting from are his three most extensive explanations of the spiritual symbolism of horns. In particular, in the first and third passages referenced he provides many pages of quotations and spiritual explanations of various passages in the Bible where horns are mentioned.
From Apocalypse Explained #316:
Horn and horns signify power, because the power of horned animals, as of oxen, rams, goats, and others, lies in their horns. That horn or horns signify the power of truth against falsity, and, in the highest sense, where said of the Lord, Omnipotence, and, in the opposite sense, the power of falsity against truth, is evident from many passages in the Word; and because it is thence evident what horns in the Word signify, of which mention is so often made in Daniel, and also in the Apocalypse, and because they are still in use in the coronation of kings, I wish to quote them.
From Apocalypse Revealed #270:
Having seven horns [Revelation 5:6]. This symbolizes the Lord's omnipotence.
The Word often mentions horns, and a horn everywhere symbolizes power. Consequently, when a horn is mentioned in connection with the Lord, it symbolizes omnipotence. Seven horns are specified, because seven symbolizes all (no. 10), thus all power or omnipotence.
From Arcana Coelestia #2832:
Horns are mentioned in various places in the Word, in which places they mean the power of truth which springs from good, and in the contrary sense the power of falsity which springs from evil.
In Swedenborg's interpretation of the spiritual symbolism of horns, then, they symbolize power, and specifically the power of divine and spiritual truth that comes from a good heart, or good intentions. And in an opposite sense (Swedenborg states that all symbols in the Bible have both a positive and a negative meaning), horns represent the power of falsity that comes from an evil heart, or evil intentions.
To put it in more human terms, when "horns of strength" are associated with a person, it means that the person is acting powerfully for the good of others using the strength of God's truth, in accordance with the Great Commandments articulated by Jesus: to love the Lord our God above all, and our neighbor as ourselves (Matthew 22:34-40).
In the opposite sense, when "horns" are used of evil power, it means that the person associated with such horns is acting powerfully to oppress and destroy others using false principles, fallacious reasoning, lies, and slander.
To "cut off the horns" (a common expression in the Bible) means to deprive of strength and power, thus rendering something (such as the altar) or someone (such as a king) weak and powerless.