あまり is a very flexible word in Japanese, that is used in several different grammar points. When paired with the ない form of a word, it translates to ‘not very (A)’, or ‘hardly (A)’. To pair
あまり (or the casual form,
あんまり) with another word, we just need to place it at the beginning of a phrase, or directly before the ない statement.
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今（いま）の時間（じかん）だったらあまり並（なら）ばないと思うよ。
At this time, I think we would not have to stand in line for very long.
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私（わたし）には犬（いぬ）がいるからあまり寂（さび）しくない。
I have a dog, so I don't feel lonely very much.
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最近（さいきん）は
どこもあまり平和（へいわ）ではない。
Recently, nowhere has been very peaceful.
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そこの肉屋（にくや）の肉（にく）はあまりいい肉（にく）ではない。
Meat from that butcher over there is hardly good.
Although あまり～ない is regularly translated as ‘not very’ the literal translation is closer to ‘not excessively (A)’. This is due to 余（あま）り (the kanji which this word comes from), meaning ‘excessive’, or ‘to be in excess’.
あまり has this meaning of ‘excessive’ in all of its grammar points, and the nuance will only change based on whether the sentence itself is positive (does not use ない), or negative (uses ない).