Compassion can be literally defined as suffering with. It is the kind of love that sees the suffering and pain of others and seeks to help through showing love and kindness. It requires us to see the suffering and hardships of others, then move to offer care and kindness in an effort to alleviate that suffering. It is something that everyone, no matter what their beliefs or faith, believe is important for humanity to succeed.
To narrow it down, consider the 3 major Abrahamic faiths. Islam, Judaism, and Christianity all teach that God is compassionate and merciful. But only Christian faith teaches that God has physically suffered with his creation in Jesus. Judaism and Islam would see such an expression of love and compassion as below God. God is compassionate, yes, but he shows his compassion from a distance compared to the compassion of Christ. This is a reason that Paul calls the cross of Jesus so offensive. The belief that God would allow himself to be so debased and dishonored to show his creation love is beyond the limits of faith and belief. Yet, that is the message of the gospel.
Paul makes this point to the Philippians (Phil. 2:1-8). In admonishing the believers there to show compassion and put others first, he raises the example of Christ who endured even death of a cross. God, seeing our need and our suffering under the powers of sin and death, chose to intervene through his own suffering and death to rescue us.