There are three kinds of meter in poetry:
Accentual-syllabic meter is the sort you're used to, in traditional English verse. The number and placement of syllables in toto, and the number and placement of accented syllables, are specified in the meter.
The most common accentual-syllabic meter for narrative verse in English is iambic pentameter. A regular line of iambic pentameter has ten syllables and five accents.
The cúrfew tólls the knéll of párting dáy,
The lówing hérd wínds slówly ó'er the léa ...
—Thomas Gray, "Elegy Written in a Country Churchyard"
In syllabic meter, we count only how many syllables are in a line. The most familiar form of syllabic poetry is the Japanese haiku. A haiku is a three-line poem with a seasonal reference; there are 5 syllables in line 1, 7 in line 2, and 5 in line 3.
In these dark waters,
Draw up from my frozen well—
Glittering of spring.
In accentual meter, we count the number of accented syllables in a line, but we can have any number of unaccented syllables. This is the characteristic meter of Old English verse.
Some poets more recently have used accentual meter. A notable example is Coleridge's Christabel, which has four accents per line, but a varying number of syllables.
'Tis the míddle of níght by the cástle clóck
And the ówls have awákened the crówing cóck;
And hárk, agáin! the crówing cóck,
Hów drówsily ít créw.
—Samuel Taylor Coleridge, Christabel