My dog on a lead.

When placed onto a lead dogs go into work mode, they will always feel like they have a job to do not only when on a lead but can feel this way if they have a coat on or when carrying something in their mouth.
If in a situation where the person holding the lead is not calm and confident that they can control any situations, the dog will then revert to it's natural pack instinct.  They will feel they have to take the leadership role, becoming defensive, aggressive if there is a perceived potential danger.
Your dog will feed from the energy that you project, they will sense the tension through the lead. You will notice a difference in behaviour once they are taken off the lead as they no in a situation to protect you, only themselves. If you feel tense or unsure of a situation your dog will then feel the need to step up and control it. This way they are not put into a situation where they need to project or control the person holding the lead - they only need to look after themselves and that is an easier situation for them to deal with.
The best way to overcome this problem is to walk your dog confidently. Your dog should always be walked behind or beside your leg, not darting ahead or to the side. This will show your dog you are in control and capable of handling any situation arising. By walking a dog this way their 'job' then becomes to behave and walk the way you want them to. This will create a much calmer, happier experience for both of you. It is a good idea to seek professional help if you are not confident and wanting some tips when walking your dog.