
It looks like Paul is repeating himself here. First he says love doesn't boast and now he says love isn't puffed up. However, after doing a little studying I found that being puffed up is a state of mind and boasting is an act that comes as a result from being puffed up.
The Greek word used here means to “puff oneself out like bellows”. Another word would be arrogance. It describes being so full of oneself that we don't accept the help of others and we don't see the needs of others. Love is aware of the needs of others and also humble enough to accept the help we are offered when we are in need.
Paul also uses this word in 1 Corinthians 8:1. He said, “We know that we all have knowledge. Knowledge makes people arrogant, but love builds them up.” Paul is not saying it's wrong to have knowledge. The best description I found for this text is that there are some who feel they have superior insight and consider themselves above ordinary people.
I've seen people drive others out of the church with this attitude. Love doesn't beat people over the head with knowledge. Instead it accepts people wherever they're at. It encourages and builds confidence in others rather than condemn them for not thinking or acting in a way we believe they should.
Love also doesn't look down at, nor act condescending towards those who have standards different from our own. None of us are better than anyone else. We all have sin in our lives and we all make mistakes. It is my belief that none of us will ever have total and complete knowledge or understanding of the Bible until we're in Heaven and God is able to explain it all to us. It is arrogant to believe we have all the answers to everything and it is arrogant to think we can change anyone. We can only accept them as they are and love them as we would love ourselves. We can introduce them to God, but He is the one who does the changing. Sometimes it is ourselves who needs to be changed and not the other person.