It means, first of all, thinking. The truth is the truth, not what you feel it is, not what you wish it were, not what matches the curtains or fails to interfere with your favorite show or keeps your friends from wrinkling their noses. Thinking is pursuit of the truth.
It means having something substantial to think about. Letting your mind flit along idly will get you nowhere. Thinking for yourself requires taking the time and effort to know those things that are worth knowing.
It does not mean removing legitimate authority and replacing it with your own opinion. It means discerning what authority is and what it is not. You are the authority on what goes on inside you, and that is no small thing. Remembering that should not fool you into thinking you are the authority on the whole wide world.
It means being willing to act on the truth when you discern it. That is the meaning of integrity. In other words, to think with the mind God gave you is a virtue, but by no means the only one or even the foremost one.
The three greatest virtues are faith, hope, and love, and the greatest of these is love. If your "thinking" leads elsewhere, you are fooling yourself with a false wisdom that exists only in your imagination.
Some people are poor thinkers, but that does not necessarily make one a poor disciple. What is important is to use the intellectual ability that you do have to discern the truth and to help others do the same. If thinking for yourself is not an extension of following the will of God, then it is as bad as not thinking at all.