Psalm 20's title says it is for the Chief Musician and is a Psalm by David. It reads like a liturgy, a worship service in which the people pray for their king, then a voice answers with confidence. The first section is a blessing: May Yahweh answer you in the day of trouble. May the name of the God of Jacob set you up on high. They ask God to send help from the sanctuary, remember the king's offerings, and grant his heart's desire.
In the second section, the mood shifts from hope to certainty: Now I know that Yahweh saves his anointed. He will answer him from his holy heaven, with the saving strength of his right hand. Anointed refers to the king whom God had chosen. Christians also notice that the title Messiah or Christ means anointed one, and in the New Testament, Peter says God anointed Jesus of Nazareth with the Holy Spirit and with power (Acts 10:38).
The third section gives the famous contrast: Some trust in chariots, and some in horses, but we trust in the name of Yahweh our God. In the ancient world chariots were like tanks, the most powerful military technology. To trust in the name of Yahweh means to rely on who God has revealed himself to be. The outcome proves the point: They are bowed down and fallen, but we rise up, and stand upright. The psalm ends with a final cry: Save, Yahweh! Let the King answer us when we call!