Strong's Concordance says the horn of the altar is the corner. Strongs also says horns are like projections on the head of an animal. Strong's number 7161 shows at least two things about the horn.

1. The horn is an actual horn that is on the head of an animal.

2. The horn is a symbol (whether in prophecy or not) of the power of a kingdom or animal.

1. Gen. 22:13 And Abraham lifted up his eyes, and looked, and behold behind him a ram caught in a thicket by his horns: and Abraham went and took the ram, and offered him up for a burnt offering in the stead of his son.

2. 1 K. 22:11, II Chron 18:10, And Zedekiah the son of Chenaanah made him horns of iron: and he said, Thus saith the LORD, With these shalt thou push the Syrians, until thou have consumed them.

3. Ps. 22:21 Save me from the lion's mouth: for thou hast heard me from the horns of the unicorns.

4. Daniel 8:3 Then I lifted up mine eyes, and saw, and, behold, there stood before the river a ram which had two horns: and the two horns were high; but one was higher than the other, and the higher came up last.

a. Daniel 8:6 And he came to the ram that had two horns, which I had seen standing before the river, and ran unto him in the fury of his power.

b. Daniel 8:7 And I saw him come close unto the ram, and he was moved with choler against him, and smote the ram, and brake his two horns: and there was no power in the ram to stand before him, but he cast him down to the ground, and stamped upon him: and there was none that could deliver the ram out of his hand.

1. Deut. 33:17 His glory is like the firstling of his bullock, and his horns are like the horns of unicorns: with them he shall push the people together to the ends of the earth: and they are the ten thousands of Ephraim, and they are the thousands of Manasseh. (This verse is speaking about the tribe of Joseph and the power this tribe will one day have.)

2. Ps. 75:10 All the horns of the wicked also will I cut off; but the horns of the righteous shall be exalted.

3. Ps. 118:27 God is the LORD, which hath showed us light: bind the sacrifice with cords, even unto the horns of the altar.

4. The horn (corner or projection) on the animal shows the power of the kingdom represented by the animal.

a. Daniel 8:3 Then I lifted up mine eyes, and saw, and, behold, there stood before the river a ram which had two horns: and the two horns were high; but one was higher than the other, and the higher came up last. (This shows the various strengths of the various kingdoms.

b. Daniel 8:6 And he came to the ram that had two horns, which I had seen standing before the river, and ran unto him in the fury of his power.

c. Daniel 8:7 And I saw him come close unto the ram, and he was moved with choler against him, and smote the ram, and brake his two horns: and there was no power in the ram to stand before him, but he cast him down to the ground, and stamped upon him: and there was none that could deliver the ram out of his hand.

d. Daniel 8:20 The ram which thou sawest having two horns are the kings of Media and Persia.

I believe the horns of the altar are projections on the corners of the altar that the sacrifices are tied to, Ps. 118:27. The corner of any structure is the strongest part. This represents the strength of the physical structure of the altar and the strength of the blood sacrifice which is on the altar.

When Adonijah (I Kings 1:50,51) caught hold of the horns of the altar, he was catching the strength, power of the altar. The same thing applied to Joab (I Kings 2:28). Both Adonijah and Joab caught hold of the horns of the altar begging for mercy for their physical lives on the strength of the spiritual (blood) sacrifice offered to God Almighty on the altar. King Solomon refused their appeal for mercy because they had both refused God's mercy for their spiritual lives through the spiritual (blood) sacrifice offered on the altar.

I Kings 22:11, II Chron. 18:10 shows Zedekiah pushing with horns of iron shows the power of Ahab's army against the Syrians. He was, of course, completely wrong. He used a holy symbol, but that didn't make his satanic predictions true.

There are many other verses in Strong's Concordance that will further prove this application to be correct. This is one very good thing about studying something as small as the horns of the altar. You never know what other good things will be revealed by such a simple (small) study.