Close-knit things are intimate, like a close-knit community where everyone knows each other's names and people look out for each other. Awww.
The adjective close-knit is perfect for describing a group of people who are socially close. A close-knit neighborhood is very different from one in which people keep to themselves and don't really know each other or have much in common with their neighbors. And a close-knit family is familiar and united in their love for each other. A good way to remember this word is to think of a tightly (or closely) knitted sweater with no gaps or holes; the people of a close-knit community stick together in the same way, leaving no opportunities for someone to "fall through the cracks."