めったに～ない is an expression that may be translated as ‘hardly’, ‘seldom’, or ‘rarely’. Originally, 滅多（めった） is a
な-Adjective that means ‘thoughtless’, or ‘reckless’. Due to this, as a 副詞（ふくし） (adverb), 滅多（めった）に literally means ‘thoughtlessly’ or ‘recklessly’.
めったに～ない will usually be paired with a verb in the negative form, or following a noun, and the 副助詞（ふくじょし） (adverbial particle) は.
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大人（おとな）になってから駄菓子屋（だがしや）にはめったに行（い）かない。
Ever since I became an adult. I hardly go to candy stores.
親（おや）とは正月（しょうがつ）以外（いがい）にはめったに会（あ）わない。
Other than New Years, I hardly see my parents.
こんなチャンスはめったにないぞ！
A chance like this is very rare.
パーティーに行（い）くことはめったにない。
I hardly do things like go to parties.
It is far more common to see めったに written without kanji, than with. However, both are used.
As
めったに originally means ‘thoughtlessly’, when appearing in a negative statement, the nuance becomes ‘to not (A) thoughtlessly’ (mindlessly, or aimlessly). This simply expresses that the speaker will not do (A) unintentionally, or (A) will not happen unless there is some special reason for it.
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私（わたし）は何（なに）か大事（おおごと）なことが起（お）きない限（かぎ）り、電話（でんわ）はめったに掛（か）けない。
Unless something big happens, I don’t mindlessly make phone calls.
家（いえ）の誰（だれ）かがテレビを見（み）ていない限（かぎ）り、自分（じぶん）からはテレビをめったに見（み）ない。
Unless someone in my house is watching TV, I don’t aimlessly watch TV on my own.