It is a noun and it has mainly two meanings.
The first meaning is “as soon as” and it is used when describing the earliest moment that something is done. "たら(すぐに)" is its milder expression.
The second meaning is "to depend on" and it is used when describing something that is based on something else. "によって/による" is its milder expression.
I’m going for a walk as soon as it stops raining.
雨が止み次第(止んだら)、散歩に行くつもりだ。
雨が止み次第(止んだら)、散歩に行くつもりだ。
Whether your Japanese gets better or not depends on how much effort you put into it.
日本語が上手くなる(or上達するか)かどうかは、努力次第だ(orどれだけ努力にするかよる) 。
日本語が上手くなる(or上達するか)かどうかは、努力次第だ(orどれだけ努力にするかよる) 。
Meg and her boyfriend are talking about their plans about a date.
- Meg : Are we still on for dinner tomorrow?
明日(の夜)、大丈夫そう？ - Kei : I have a meeting until 6 and it may be extended. Whether I can make it on time or not depends on the situation.
6時まで会議があって、長引く(or延びる)かも。間に合うかどうかは、その状況次第だな(or状況によるな)。 - Meg: Okay, then can you text me as soon as you finish your work?
わかった。じゃあ、仕事が終わり次第(終わったすぐに)、メールして。
Meg and Amy are gossiping.
- Amy : I think that Leo looks better than ever. What do you say?
レオが格好良くなったと思わない？ - Meg : He is cute, but I saw him cheating on his girlfriend last weekend.
格好良いけど、先週浮気しているのを見ちゃった。 - Amy : Really? I don't think that he is a kind of person who would let her down.
本当？彼女を裏切るような人には見えないよ。 - Meg : Whether you believe it or not is up to you. You can't judge people by appearances.
信じるか信じないかは、エイミ次第だけど、人は外見で判断できない。