The adverb everywhere means in all possible places. If you take your phone with you everywhere you go, it means you have it with you in all the places you travel.
You can use everywhere literally, but it's probably more common to use it in an exaggerating way. For example, if you can't find your glasses, you might say, "I've looked everywhere for them!" You haven't actually looked everywhere, in every possible place — you've actually only looked in all the places you think you might have left your glasses. In Old English, it's æfre gehwær.