I think there are different ways to answer this, which will often depend on what modality the counsellor’s training is in. My personal definition, however, would be that counselling is time and space in which to share your thoughts and feelings with someone without fear of judgement. It is a professional relationship, but one based on compassion and understanding that has the potential to be one of the closest relationships you have ever experienced. It isn’t about the counsellor fixing things for you, though they may share observations, questions or challenges that could send your thinking down a different route to one you might have reached on your own.
Likewise, there isn’t always an absolute objective to counselling – it is what you make it. A very general catch-all objective to most counselling might be to ‘feel better’ or ‘explore yourself’, or indeed a combination of the two, but in reality it can be as specific as stopping a particular behaviour and as general as just having somewhere to share thoughts. It’s often helpful if you go into counselling with some idea of what you want to get out of it, though, so that the work has a goal to work towards.