Although written almost exclusively in hiragana, せい is a 名詞（めいし） that may be better understood from its kanji, 所為（せい）, meaning ‘doings’. せい is used to convey negative results that occurred due to the behavior or actions of another person/thing. Because of this, common translations of せい are ‘fault’, ‘due to’, or ‘because of’.
As せい is a noun, it may be used after the 連体形（れんたいけい） (attributive form) of any other word. The 格助詞（かくじょし） (case marking particle) で will also regularly be seen after せい, especially when conveying the (B) result that occurred ‘with’ or ‘by means of’ those ‘doings’.
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昨日（きのう）夜（よる）遅（おそ）くまで起（お）きていたせいで寝坊（ねぼう）した。
Because I stayed up late last night, I overslept today.
外（そと）が寒（さむ）いせいで風邪（かぜ）を引（ひ）いた。
Because it is chilly outside, I caught a cold.
犬（いぬ）の手術（しゅじゅつ）の事（こと）が心配（しんぱい）なせいで今日（きょう）は寝（ね）れなさそう。
Due to me being worried about my dog's surgery, it doesn't seem like I am going to be able to sleep.
大雪（おおゆき）のせいで道（みち）が渋滞（じゅうたい）してる。
Because of the heavy snow, the road is congested.
The ‘doings’ that 所為（せい） represents is similar to the negative ‘doings’ that is used in English to place blame. This can be seen in phrases such as ‘it was the weather's doings’, or ‘ah, so the missing cookies were your doings!’
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遅刻（ちこく）したのは渋滞（じゅうたい）のせいだ！
Me being late is the traffic’s doing!
台風（たいふう）のせいでまた予定（よてい）が変（か）わったよ。
Due to the typhoon’s doings, my plans have changed again.