Psalm 28:2 is a heartfelt plea to God for attention and favor. Let's break down the meaning of each part:

"Hear the voice of my petitions..." This signifies a desperate request to God. The psalmist isn't just praying in general; they have specific needs and requests ("petitions") that they urgently want God to hear. The word "voice" emphasizes the sincerity and intensity of their prayer.

"...when I cry to you..." This reinforces the urgent and distressed nature of the psalmist's prayer. "Crying" suggests a louder, more impassioned plea stemming from deep emotional need or suffering. It indicates that the situation is serious, and the psalmist is reaching out to God in desperation.

"...when I lift up my hands toward your Most Holy Place." Lifting up hands was a common posture of prayer in ancient times, signifying submission, supplication, and a reaching out to God. The "Most Holy Place" refers to the innermost sanctuary of the Temple in Jerusalem (or, metaphorically, to God's dwelling place in heaven). By directing their gesture toward this sacred location, the psalmist is acknowledging God's holiness, power, and authority, and indicating their desire to connect with God in a reverent and meaningful way. It also represents a longing to be in God's presence and receive His blessings.

In summary, this verse is a powerful expression of:

Urgent need and dependence on God: The psalmist is in a difficult situation and knows they need God's help.
Sincere and heartfelt prayer: The language suggests a deep emotional connection and a genuine desire to be heard.
Reverence and submission to God: Lifting hands toward the Most Holy Place acknowledges God's holiness and authority.
Faith in God's ability to answer prayer: The psalmist believes that God can and will hear their petitions.

The overall meaning is a desperate cry for God's attention and intervention, offered with reverence and faith.