Daniel prays in complete humility. He prepares himself by fasting, he dressed in sack cloth, and with ashes. Israel sinned against God, this is why God allowed the Assyrians to conquer the north, and the Babylonians take the south. In captivity, they did not repent. but God as usual is faithful and convenant keeping, He keeps to His promise to return the Israelites to their land after 70 years of punishment. Daniel is coming to God to intercede for all Israel, he takes this humble stance in his prayer. He confesses to the sins of Israel, Jesus Christ did the like for the world too.
When we take it upon ourselves to intercede for others, we must be sure that we are in a right relationship with God. We must have our own houses in order, first. We can not presume that by praying for others that we will make things right between us and the Lord. We need to have the right standing with our God so that we don't put others into trouble while interceding for them. Fasting is also essential, in filling of the Holy Spirit.