When cooks baste food, they brush or drizzle a savory liquid on it as it's cooking. If you baste your Thanksgiving turkey while it bakes, it will stay moist and tender.
A chef might baste grilled vegetables with their marinade, or baste roasting meat with its own oily drippings. The technique keeps food from drying out as it cooks. Another meaning of baste is "to sew loosely." You might quickly baste the hem of a curtain before stitching it securely in place. The origin of the culinary baste is a bit of a mystery, but the sewing term comes from the Old French bastir, "construct" or "sew up."