Specifically, sonnets often use iambic pentameter, which is a metrical pattern consisting of five iambs per line. An iamb is a metrical foot with one unstressed syllable followed by one stressed syllable.
For example, the line "Shall I compare thee to a summer's day?" from Shakespeare's Sonnet 18 follows iambic pentameter:
* Shall (unstressed) I (stressed) com (unstressed) pare (stressed) thee (unstressed)
* to (unstressed) a (stressed) sum (unstressed) mer's (stressed) day (unstressed)
So, while meter is the general term, iambic pentameter is the specific rhythm often found in sonnets.