まま, coming from the kanji 儘（まま）, which means ‘as it is’, is a 名詞（めいし） in Japanese that is used for describing the ‘unchanged state’ of something. This expression may be translated as ‘while remaining (A)’, ‘as (A) is’, or ‘left in the state of (A)’. It can be used after any word in its 連体形（れんたいけい） ‘attributive form’. However, when used with verbs, it has a tendency to be used with the た (past) form most frequently.
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うぁ〜、マジかよ。電気（でんき）とガスを点（つ）けたままだった。
Whaaat. Are you serious? I left my gas and electricity on.
部屋（へや）を汚（きたな）いままにしていたらゴキブリが沢山（たくさん）出（で）てきた。
So many cockroaches appeared because I left my room dirty.
いつまでも元気（げんき）なままでいてね。
Please always stay healthy, okay?
今（いま）のままだと、一生（いっしょう）結婚（けっこん）できないと思（おも）うよ。
If you are the way you are now, I don't think you'll ever be able to marry.
まま often expresses that something should be left alone, or undisturbed. This is generally seen with verbs in the ない form.
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許可（きょか）を取（と）らないまま駅（えき）で撮影（さつえい）をしていたら、警察（けいさつ）が来（き）た。
While I was filming without getting a permit, the police were called.
夕食（ゆうしょく）を食（た）べないまま寝（ね）たら、お腹（なか）が空（す）いて3時（じ）ぐらいに起（お）きてしまった。
Because I slept without eating dinner, I woke up at 3 am from hunger.
While
まま may be followed by the 格助詞（かくじょし） (case marking particle)
に, it is very often omitted. When it appears, however, it will place extra emphasis on the next verb in the sentence.
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エンジンを点（つ）けたままにしておいてください。
Please keep your engine on.
扇風機（せんぷうき）を点（つ）けたままにして家（いえ）を出（で）る。
I leave my house with my fan turned on. (Often)