Romans 14:5,6 - Each one should be fully convinced in his own mind

14:5

Paul now moves on from food to observing special days. The days in questions are probably the Sabbath. So some saw the Sabbath (I suppose it could be either Saturday or Sunday) as special, others saw all days as equally special. Paul’s instruction is that each person should make up his own mind. 

14:6

As long as someone has settled the matter in their own mind and is acting to honour the Lord, then that is fine. We should note that we are not talking about matters where something is clearly forbidden. But in these matters which are not absolute the conscience of the individual is what matters. Whatever we do we are to do it in order to honour the Lord. Paul then goes back to food. The one who eats meat does so with thankfulness to God, the one who abstains does so in honour of the Lord.