to "feel a need" means simply to want, or to desire strongly, or to long for something. Used in a sentence one might say "I felt the need to tell you that you are such a lovely person." or "I feel the need to say something that I have been keeping silent for some time." or "I have always felt the need to go to Florida at some point in my life." There are countless ways you can use it, so if you have any more questions, feel free to ask !