What does it mean to train and test a data for feature extraction?
This is a concept in supervised machine learning.

Train data: Used to train your supervised ML model. This data contains both the input and the desired output, which is compared with the output from your model. Your model is hence trained to reduce the prediction error or cost function.

Test data: The data for which you want to predict the outcome. The desired output is unknown. Based on the training data, your model predicts outcome for the new test data.

You should become more familiar with the concepts of machine learning first, before asking questions here. There is a plethora of resources on machine learning.