Kinship is a triggered ability found on a handful of Lorwyn-block creatures. At the beginning of your upkeep, you look at the top card of your library. If it shares a creature type with the creature that has kinship, you may reveal it and get the listed bonus (effects vary by card). Whether you reveal it or not, that card stays on top of your library—it's never drawn or shuffled away by kinship itself.
The most common mistake: people think kinship draws the card or moves it. It doesn't. You simply peek, optionally reveal for the effect, then leave it on top, so you'll draw it next.
In Commander, kinship rewards tribal decks where most of your library shares a type—if nearly every card is, say, an Elf, you reliably hit. It also pairs nicely with top-deck manipulation (scry, Sensei's Divining Top) to guarantee the trigger each turn.