There's two ways- 

1. You could feel too strongly about the significance of something which could result in anxiety and fears because of its importance to you. Like a relationship or a job that meant everything to you until it ended. The feeling of significance therefore will be useful in some contexts and harmful in others. 
2. This is related to the intellectual idea of meaning. If you have a strong set of ideas about what something means, it can prevent you from seeing it in different perspectives which might be necessary to solve certain problems.

In politics or in your personal life, you may feel powerless, or there may be situations which are not in your control but you would still get anxious and wouldn't be able to stop thinking about it. This shows an excess in meaning because if you genuinely didn’t feel the situation was significant you wouldn’t worry about it. 

In the intellectual context, if your ideas and reasoning of the world is rigid you will get stuck when you encounter situations that fail to make sense for you.

Mindfulness, particularly the body-scanning methods popular among Vipassana retreats, are effectively, a way of reducing the emotional and intellectual excesses of meaning. 

By repetitive attention something that would be processed at a level of meaning dissolves into parts that lack that meaning and you start experiencing something that seems to lack connection to the meanings you had previously.

However, this may be a consequence of the thorough de-meaning-ization of your regular experience. 

Meanings are an important part of living life well. What’s necessary is that, from time to time, you should be able to temporarily “relax” your meanings in life. 

These meaningness relaxations may be related to specific situations (i.e. how you think about your future career) or it could be more global (i.e. should you find meaning in ambition at all?).

The new meanings you get to may not be any better but they may help you see around obstacles that keep you from living a good life.