As Muslims we need to make sure we’re spreading peace to everyone around us. This hadith was when the Prophet (saw) had arrived in Madinah and was instructing people on how to behave and what a proper Muslims etiquette should be. It is through our peaceful character that people will become attracted to Islam. Peace can be attained through any virtuous deed that purifies the heart. As long as the peaceful action helps promote peace in society, households, etc. Every teaching in Islam is based on peace and avoidance.
From this hadith we see how Islam promotes community service and acts of goodwill in society. Many times these acts go unnoticed for the actions we often perceive as being greater in the sight of Allah (swt). Feeding the hungry is an important part of Islam.
Praying at night has its own virtues. The Prophet (saw) mentions it specifically in this hadith to single out this act since only those with sincere intentions will pray at night. This hadith encompasses all of the acts of worship that need to be done with a clean and pure heart.