Counter is a confusing term in Magic as it has several definitions. In terms of being a 'keyword' it refers to a marker placed on an object, usually modifying its characteristics. Counters with the same name or description are interchangeable. Counters may also be given to players, like poison counters.
If a permanent has both a +1/+1 counter and a -1/-1 counter on it, N +1/+1 and N -1/-1 counters are removed from it, where N is the smaller of the number of +1/+1 and -1/-1 counters on it.
Example: A creature has three +1/+1 counters and it receives two -1/-1 counters, it then ends up with just one +1/+1 counter, removing the four other counters.