“Blessed is the man who has his quiver full of them.” The man’s household is compared to a quiver that keeps arrows protected and close by, ready for action. At a time when there was no police force to provide protection, and no government that provided people support in their old age, a large family, and especially lots of sons, was a person’s best hope for having a comfortable old age.
“They will not be put to shame.” The “they” refers to the father and his sons who are supporting him.
“when they speak with their enemies at the gate.” In this instance, the word “speak” is a synecdoche (the part for the whole), because if a man has “enemies,” his sons will do more than just “speak” to them, although most confrontations would start with speaking. At a time when family members defended family members, if a father had enemies, the sons would do whatever it took to defend and protect the family.