“It'll keep in the fridge for about... 3 or 4 days?”
You made a traditional dish from your country and brought some for one of your coworkers. When you give it to her, you tell her how quickly she should eat it.
It'll keep in the fridge for about... 3 or 4 days?
His landlord reassured him that it was only a temporary inconvenience. "It'll be ready by Monday," he said.
"It'll" is similar to "this'll" and "that'll". All of these contractions are less common and less formal than the usual contractions like "can't" and "isn't".
English speakers usually call their refrigerator "the fridge". For example:
I have some beers in the fridge. You want one?
The word "refrigerator" sounds a bit formal. You say "refrigerator" when you're talking about it as a machine. For example, when you're calling a repairman:
Can someone come out and take a look at my refrigerator? It's not staying cool like it's supposed to.
Food eventually "goes bad": it becomes rotten, stale, or rancid. It's not safe to eat after a certain period of time. You can talk about that time period by saying that the food "will keep for ___":
A jar of honey will keep for decades if it remains sealed.
It will keep in the freezer for a couple of months.