N4
て(理由)
て(りゆう)
Because ~, ~ and so (a light reason with the て / で form)
今日は宿題が多くて行けなかった。
I couldn't go today because I had a lot of homework.
Explanation
Joining two clauses with the て-form can show that the first is the reason for the second: 「ニュースを聞いて、びっくりした」 (I was surprised to hear the news), 「頭が痛くて、勉強できない」 (I have a headache, so I can't study). It is a light way to give a reason, and what follows must be something outside your will: a feeling (「嬉しい」, 「困る」), a body reaction (「疲れる」) or something you cannot do (「間に合わない」).
Mixed up with
Do not use it when the second part is a request, an invitation, a wish or a command. Use 「から」 or 「ので」: 「時間がないから、急ぎましょう」 is right, 「×時間がなくて、急ぎましょう」 is wrong.
For a negative reason use only 「〜なくて」: 「会えなくて寂しい」 (I'm lonely because I can't see you). 「〜ないで」 describes an accompanying state, not a reason.