Hadith: When the Messenger of Allah (may Allah's peace and blessings be upon him) and his Companions went to Makkah, the polytheists said: "There will come to you people who are weakened by the fever of Madīnah." So, the Prophet (may Allah's peace and blessings be upon him) commanded his Companions to jog the three rounds (of Tawāf) and walk between the two Corners.

عن عبد الله بن عباس رضي الله عنهما قال: «لَمَّا قَدِم رسُول الله -صلَّى الله عليه وسلَّم- وأصحابه مكة، فقَال المُشرِكُون: إِنَّه يَقدَمُ عَلَيكُم قَومٌ وَهَنَتهُم حُمَّى يَثرِب، فَأَمَرَهُم النَّبيُّ -صلَّى الله عليه وسلَّم- أن يَرمُلُوا الأَشوَاطَ الثلاَثَة، وأن يَمشُوا ما بَين الرُّكنَين، ولم يَمنَعهُم أَن يَرمُلُوا الأَشوَاطَ كُلَّها: إلاَّ الإِبقَاءُ عَليهِم».
[صحيح] - [متفق عليه]

‘Abdullāh ibn ‘Abbās (may Allah be pleased with him) reported: When the Messenger of Allah (may Allah's peace and blessings be upon him) and his Companions went to Makkah, the polytheists said: "There will come to you people who are weakened by the fever of Madīnah." So, the Prophet (may Allah's peace and blessings be upon him) commanded his Companions to jog the three rounds (of Tawāf) and walk between the two Corners. He did not command them to jog all the rounds out of pity for them.
Sahih/Authentic. - [Al-Bukhari and Muslim]

Explanation

The Prophet (may Allah's peace and blessings be upon him) went to Makkah in the sixth Hijri year, along with many of his Companions, to perform ‘Umrah. The Quraysh disbelievers went out to fight him and bar him from the House of Allah, but, a treaty was concluded between the two sides. As stipulated by the treaty, the Prophet (may Allah's peace and blessings be upon him) and his Companions had to return home that year and come back to Makkah the following year to perform ‘Umrah and stay there for three days. They came in the seventh year to perform ‘Umrah. Thereupon, the polytheists, gloating and giving vent to their feelings of revenge, said to one another: There will come to you people who are weakened and enfeebled by the fever of Madīnah. When this reached the Prophet (may Allah's peace and blessings be upon him), he, seeking to rebut their statement and vex them, ordered his Companions to quicken their pace as they performed the Tawāf rounds, except between the Yemeni Corner and the Black Stone Corner, where they could walk normally. He did so out of mercy and pity for them and because the disbelievers, who climbed Mount Qu‘ayqi‘ān to see the Muslims as they performed Tawāf, would not be able see them when they were between the two Corners. Vexed, the disbelievers said: "Indeed, they are but like gazelles." Hence, this jogging became a Sunnah to be observed in Tawāf upon arrival in Makkah, in memory of the situation of our righteous predecessors. This is also to follow their footsteps in their praiseworthy stances, firm perseverance, and the glorious acts they did to support this religion and make the word of Allah superior. May Allah guide us all to follow their example and footsteps!