Ahimaaz, from the Hebrew name pronounced awkh-ee-mawh-awtz (notice how actual names in Hebrew frequently sound very different than how they are rendered into English) was the son of Zadok, a high priest at the time that King David's son Absalom staged a revolution against his father. During that time of Satanic anarchy, Ahimaaz and the LORD's anointed high priesthood remained loyal to the LORD's anointed king - a profound demonstration of the Messianic ("Messiah" and "Christ" mean anointed one) singularity of both positions. The human high priest, and human king of Israel, represented Jesus Christ (see the Fact Finder question below).
"3:1 Wherefore, holy brethren, partakers of the heavenly calling, consider the Apostle and High Priest of our profession, Christ Jesus: (Hebrews 3:1 KJV)
"18:37 Pilate therefore said unto him, Art thou a king then? Jesus answered, Thou sayest that I am a king. To this end was I born, and for this cause came I into the world, that I should bear witness unto the truth. Every one that is of the truth heareth my voice." (John 18:37 KJV)
"7:1 For this Melchisedec [see Melchizedek], king of Salem, priest of the most high God, who met Abraham returning from the slaughter of the kings, and blessed him; 7:2 To whom also Abraham gave a tenth part of all; first being by interpretation King of righteousness, and after that also King of Salem, which is, King of peace; 7:3 Without father, without mother, without descent, having neither beginning of days, nor end of life; but made like unto the Son of God; abideth a priest continually." (Hebrews 7:1-3 KJV)
"The running of the foremost is like the running of Ahimaaz the son of Zadok"
David's vain and disloyal son Absalom manipulated the "politics" of the kingdom to his own favour ("stole" the hearts is a very accurate term i.e. "15:6 And on this manner did Absalom to all Israel that came to the king for judgment: so Absalom stole the hearts of the men of Israel" 2 Samuel 15:6 KJV). When the treachery ripened into an outright takeover, David was forced to flee the capital.
As explained above, the high priesthood at the time recognized their place and purpose, so when they saw the political capital leaving, they began the removal of the religious capital as well. With the king, went the Ark of the Covenant, moved by the Levites who were authorized to carry it (see Raiders Of The Lost Ark to understand why it is that who could move the Ark is a key to understanding where it is today), including Ahimaaz. David ordered them to return the Ark to the city however. David was a fighter, not a defeatist. He was merely making a strategic retreat prior to the coming battles in which he would recover the position that the LORD had assigned to him. He knew that victory was guaranteed because Absalom was rebelling against the LORD's anointed, and therefore the LORD Himself.
"15:23 And all the country wept with a loud voice, and all the people passed over: the king also himself passed over the brook Kidron, and all the people passed over, toward the way of the wilderness.
15:24 And lo Zadok also, and all the Levites were with him, bearing the ark of the covenant of God: and they set down the ark of God; and Abiathar went up, until all the people had done passing out of the city.
15:25 And the king said unto Zadok, Carry back the ark of God into the city: if I shall find favour in the eyes of the LORD, he will bring me again, and show me both it, and his habitation:
15:26 But if he thus say, I have no delight in thee; behold, here am I, let him do to me as seemeth good unto him.
15:27 The king said also unto Zadok the priest, Art not thou a seer? return into the city in peace, and your two sons with you, Ahimaaz thy son, and Jonathan the son of Abiathar.
15:28 See, I will tarry in the plain of the wilderness, until there come word from you to certify me. 15:29 Zadok therefore and Abiathar carried the ark of God again to Jerusalem: and they tarried there." (2 Samuel 15:23-29 KJV)
As instructed by David, Ahimaaz and the other Levites served as David's eyes and ears in the city. Ahimaaz was also one of the Levites who served as a swift runner for communications (note also that the Levites were physically fit - they did not use their study and "religious" life to become weak).
"15:35 And hast thou not there with thee Zadok and Abiathar the priests? therefore it shall be, that what thing soever thou shalt hear out of the king's house, thou shalt tell it to Zadok and Abiathar the priests.
15:36 Behold, they have there with them their two sons, Ahimaaz Zadok's son, and Jonathan Abiathar's son; and by them ye shall send unto me every thing that ye can hear." (2 Samuel 15:35-36 KJV)
When Absalom's rebellion was defeated, with the killing of Absalom himself, Ahimaaz was one of the runners who were sent to deliver the news to David.
"18:19 Then said Ahimaaz the son of Zadok, Let me now run, and bear the king tidings, how that the LORD hath avenged him of his enemies.
18:20 And Joab said unto him, Thou shalt not bear tidings this day, but thou shalt bear tidings another day: but this day thou shalt bear no tidings, because the king's son is dead.
18:21 Then said Joab to Cushi, Go tell the king what thou hast seen. And Cushi bowed himself unto Joab, and ran.
18:22 Then said Ahimaaz the son of Zadok yet again to Joab, But howsoever, let me, I pray thee, also run after Cushi.
And Joab said, Wherefore wilt thou run, my son, seeing that thou hast no tidings ready?
18:23 But howsoever, said he, let me run.
And he said unto him, Run. Then Ahimaaz ran by the way of the plain, and overran Cushi.
18:24 And David sat between the two gates: and the watchman went up to the roof over the gate unto the wall, and lifted up his eyes, and looked, and behold a man running alone.
18:25 And the watchman cried, and told the king.
And the king said, If he be alone, there is tidings in his mouth. And he came apace, and drew near.
18:26 And the watchman saw another man running: and the watchman called unto the porter, and said, Behold another man running alone.
And the king said, He also bringeth tidings.
18:27 And the watchman said, Me thinketh the running of the foremost is like the running of Ahimaaz the son of Zadok.
And the king said, He is a good man, and cometh with good tidings.
18:28 And Ahimaaz called, and said unto the king, All is well. And he fell down to the earth upon his face before the king, and said, Blessed be the LORD thy God, which hath delivered up the men that lifted up their hand against my lord the king.
18:29 And the king said, Is the young man Absalom safe?
And Ahimaaz answered, When Joab sent the king's servant, and me thy servant, I saw a great tumult, but I knew not what it was.
18:30 And the king said unto him, Turn aside, and stand here. And he turned aside, and stood still.
18:31 And, behold, Cushi came; and Cushi said, Tidings, my lord the king: for the LORD hath avenged thee this day of all them that rose up against thee.
18:32 And the king said unto Cushi, Is the young man Absalom safe?
And Cushi answered, The enemies of my lord the king, and all that rise against thee to do thee hurt, be as that young man is.
18:33 And the king was much moved, and went up to the chamber over the gate, and wept: and as he went, thus he said, O my son Absalom, my son, my son Absalom! would God I had died for thee, O Absalom, my son, my son!" (2 Samuel 18:19-33 KJV)
Fact Finder: (a) Is the Messiah our High Priest? (b) Is the Messiah our King?
(a) See What Is Jesus Christ Doing Right Now?
(b) See Israelite Monarchy - The Messiah