Feature engineering is like cooking. You have a recipe for a dish and ingredients to use, but to make it taste the best, you might want to add some extra spices or change the way you cut the ingredients.
The same goes for machine learning. You have data that you want to use to make predictions, but to make the predictions as accurate as possible, you might want to create new information from the data that you already have. This new information is called features, and the process of creating them is called feature engineering.
Just like a chef needs to understand what ingredients go well together and what flavors they'll create, someone doing feature engineering needs to understand the data they're working with and what new information they can create that will help the machine learning predictions be better.
That's where domain expertise comes in - it's like having a really good cook in the kitchen who knows a lot about the dish you're making and can help make it even better. A domain expert has a lot of knowledge about the problem you're trying to solve and the data you're using, and this can help guide the process of feature engineering to make it more effective.