This is the 7544th most frequent Chinese word.
记
"记" means "to remember," "record," or "note."
In this sentence, 记 is used as 'note down' or 'record', shown in the verb phrase 记下.
请你记下我的电话号码。
Please write down my phone number.
Here, 记 implies 'to take note of', indicating the action of paying attention to and remembering details.
你上课要记好老师讲的内容。
You should take careful notes of what the teacher says in class.
Here, 记 is used in the sense of 'recall' or 'remember', embedded in the compound verb 记得.