Breadth of chest means to be big spirited.  Just like the tyres of a tractor is able to withstand a rough surface and not get damaged, as opposed to that of the common individual who is more like the tyre of a bicycle that can withstand considerably less hindrance and can easily be damaged.

Imam Ali peace be upon him, said “The means to secure high authority is breadth of chest (i.e., generosity).”

([وقال عليه السلام : آلَةُ الرِّيَاسَةِ سَعَةُ الصَّدْرِ, ([1

so an obligatory requirement for accepting responsibility is to be able to with stand bumps along the way.

A supplication by Prophet Moses peace be upon him, once he reached the position of prophet hood was to request breadth of his chest and asked Allahﷻ to “expand my breast” ([2]):

{قَالَ رَبِّ اشْرَحْ لِي صَدْرِي}

Of course, Prophet Moses peace be upon him, requested this and Allahﷻ provided this to him, however, it should be noted that this was granted before any request from the Prophet blessings be upon him and his Purified Household:

{أَلَمْ نَشْرَحْ لَكَ صَدْرَكَ}

“Did We not expand thy breast for thee”.([3])

[1] Nahjul Balagha Hikmat 176

[2] Surah Ta Ha 20:25.

[3] Inshirah 94:1