This paper will explain the basics. So much for the dictionary. As used in church hymns, metre is simply the pattern of syllable counts in the lines of a verse.
Short metre has two less syllables on the first line.
The pattern is therefore 6,6,8,6. Long metre is 8,8,8,8. Here is an example of long metre, this time without the numbers. Other metres, of which there are many, are simply referred to by their pattern. Something is needed to break the monotony, or to delay its onset.