to remember as a verb is a mental action = recordarse ex. i remember my last trip to Spain, i still remember my childhood friend to remain as a verb = quedarse ex. her memories remain the same in my mind please check www.dictionary.com

Remember means to have or keep an image or idea in your mind of (something or someone from the past) or to think of (something or someone from the past) whereas remain means stay/ continue in the same state or condition.