I always say, if you see someone meditating he could be doing 100 different things but I generally put it in 2 categories: cleaning up or being at peace. we have a lot of baggage within us which rob us of inner peace. certain forms of meditation help to make peace with our traumas and unresolved emotions , those i call cleaning. its hard to sit and be at peace in a chaotic space. the more we clear our emotional relationship with life and the more easy it is to sit in peace.
as for sitting in peace its for both resting the mind and refocusing the mind in a more constructive, pleasant state so we can go back to dealing with life. first , for calming the body I like to give each part of bady a bit of attention and intentionally relax each part. like all will say, if there are floating thoughts that doesn't mean faillure, they are just floating thought , be aware of them but don't pay them too much attention, let them float away on their own. to clear my mind I like 2 techniques. one technique is when you are sitting, eyes closed, watching the darkness and the floating thought, try to see where the new thoughts come from, if you do it right it pretty much ends all thoughts right there but its hard to maintain. another way is to carefully observe the breathing and when you have done this for a while you realise that you are not your thoughts, you are what is watching the thoughts. that is the watcher, the true self, the part of us which only is , just becoming aware that what you are is pure awareness makes you come back to the part of your self which is always at peace. this is called the self-inquire meditation. it is one of the methods thought by ramana maharshi, one of the most respected masters from the neo-advaita non-dualist school of thought. meditation done right is not an effort, its a spiritual vacation, it should feel like your mind is sitting in a jaccuzi. its oneness and bliss.