What is the meaning of Shafa'ah (Sunni view)?

There is some narration from Prophet Muhammad (PBUH) installed in Masjid an Nabawi in Madinah, justified as "Sahih"(=Correct) or "Hassan"(=Well) in different Sunni references: > النَّبِيِّ صلى الله عليه وسلم قَالَ ‏:‏ ‏ "‏ **شَفَاعَتِي** لأَهْلِ الْكَبَائِرِ مِنْ أُمَّتِي ‏"‏ > >The Prophet (PBUH) said: My intercession (*shafa'ah*) will be for those of my people who have committed major sins. Sunan Abi Dawud 4739 , Jami at-Tirmidhi 2435 , and also 2436 . What is the idea of Sunni brothers about "Shafa'ah"? Who can do "Shafa'ah"? Is it Shirk to ask prophet's Shafa'ah?