It is a noun that means "procrastination". It is used when you put off something that has to be done because it is unpleasant or boring. "先延ばし" is a synonym for "後回し" and they are interchangeable in many cases, but the nuance is slight different.
The focus of "先延ばし" is the postponement of something, but the focus of "後回し" is the priority of things and it indicates that you do something else instead of something.
If you are interested in "先延ばし", please click HERE
The deadline for submission of the report is approaching.
- Meg : Have you submitted the report yet?
もう報告書は提出した？ - Amy : Not yet. I've been putting it off for a while.
まだ。ずっと先延ばし(or後回し)にしているんだよね。 - Meg : Me neither. I'm going to stay up all night working.
私も。徹夜でやろうかな。
Amy is calling her boyfriend because she waited for him but he didn't show up.
- Amy: When can you come here?
いつ来れそう？ - Jim: Sorry. Something came up, so I won't be able to come.
ごめん。用事が出来て、行けなくなっちゃった。 - Amy: Again? You said that I am more important than anything else, but I always come last.
また？私が一番大事って言ったのに、いつも私は後回しじゃん。
Meg and her boyfriend are talking about their future.
- Tom: I want to marry you. I thought you feel the same way, I was wrong, right?
メグと結婚したい。メグも同じ気持ちだと思っていたけど、違うんでしょ？ - Meg: No. Just like you, I want us to be together.
ううん。私もトムと一緒にいたいよ。 - Tom: So, why are you transferring to the Hong Kong branch? Do you think our relationship will work out?
じゃ、なんで香港支社に転勤するの？俺たち(の関係)、続けられると思う？ - Meg: I'm not sure about it. I've got my hands full with all the tasks in front of me, but I don't want to put my dream on the back burner anymore. I want to work there.
わからない。目の前の仕事をこなしてきたけど、もうこれ以上、自分の夢を後回しに出来ないよ。行きたいの。