Idiom: to look after (something/someone); used as a verb.
First Example: Herb was going on vacation, but he was worried about his cat, so he asked Cindy to take care of it. She agreed, and she looked after his cat while Herb was out of town.
Meaning: "to look after (something)" means to take care of something, often something that isn't yours. In this example, Cindy is taking taking care of Herb's cat while he's out of town. This idiom can apply to any situation where someone takes care of something else, but it's usually used for people and things that can't take care of themselves or are likely to get into trouble (such as an animal, a child or an elderly person). It's used in the simple past tense in this example to explain that she isn't caring for the cat anymore.
Here is another example:
Second Example: Both of Billy's parents work, and they don't get home until after 6:00 pm. Billy is old enough to be alone, but his little sister, Melody, isn't, so Billy looks after Melody until his parents get home.
Meaning: In this case, Billy is looking after his little sister, who is too young to take care of herself and might get into trouble if left alone. This idiom can be used for short-term care (such as the first example, which only happened for a few days/weeks) or long-term care (such as this example, which happens every school day). In this example, it's used in the simple present tense to clarify that Billy regularly does this.
This idiom is from LSI's book "Speaking Transitions," which is used in the Level 4 Listening/Speaking classes.