to obey: to hold to a command or teaching and put it into practice
This is the most common use of the word in the New Testament, and the one that shapes how people live. To keep a command, or to keep someone's word, is not merely to remember it or agree with it. It is to guard it carefully and act on it, so that the command stays unbroken in the way you live.
Jesus uses this word again and again to tie love to obedience: those who love him keep his words, and those who keep his commands are the ones who truly know God. John's letters press the same point, testing real faith by whether a person actually keeps God's commands rather than only claiming to.
The word carries a sense of watchful care, not grudging compliance. You keep a command the way a faithful person keeps a trust: attentively, completely, and over the long haul. Breaking one part of the law is described as failing to keep the whole of it, because the keeping is meant to be entire.