Psalm 20:3 is a prayer offered on behalf of a king or leader before battle. Let's break down the verse to understand its meaning:

"Remember all your offerings...": This refers to the sacrifices the king has made to God in the past. The speaker is asking God to recall these acts of devotion and obedience. In the Old Testament, offerings and sacrifices were a tangible way to demonstrate faith, repentance, thanksgiving, and dedication to God.
"...and accept your burned sacrifice.": Specifically mentions "burned sacrifice," which was a type of offering where the entire animal was burned on the altar as a complete offering to God. The act of burning symbolized complete surrender and dedication to God's will. The speaker is pleading for God's favor by asking Him to accept this particular sacrifice as a sign of the king's sincere devotion.
"Selah": This word appears frequently in the Psalms. Its exact meaning is debated, but it's generally understood as a musical direction or a pause in the text for reflection. It might indicate a moment to contemplate the prayer's meaning or for musical interlude.

In essence, the verse is a prayer for God to:

Acknowledge and appreciate the king's past acts of worship and obedience.
Favorably receive the king's current sacrifice as a symbol of his dedication.
Show grace and grant success in the upcoming endeavor (likely battle).

Deeper Implications:

The verse highlights the importance of:

Past faithfulness: The prayer acknowledges that past devotion matters to God.
Present dedication: The offering of the burned sacrifice demonstrates a present commitment.
Seeking God's favor: The verse emphasizes the dependence on God's blessing for success.

Application:

While we no longer offer animal sacrifices, the principles remain relevant. The verse encourages us to:

Live a life of consistent devotion to God.
Offer our "sacrifices" of praise, service, and obedience as acts of worship.
Depend on God's grace and favor in all our endeavors.