The subjective world is our very personal view of the world. It is entirely our own. For example, I like coffee. The taste and smell of coffee, and the feelings of satisfaction and pleasure I have on drinking it are entirely my own. I could try to explain using language what these sensations and feelings are but I would never really succeed. Even if another person responds, "that's exactly what I feel and sense" we can never be sure that we have exactly the same sensations and feelings. What the person and I would actually be comparing are a set of descriptive words, but we could be associating these words with altogether different sensations of drinking coffee.
Another example is colour. When we see the colour "red", say, we may all recognise it as the colour red simply because we are taught to recognise colours from early childhood. But the actual sensation of seeing the colour red is entirely an individual matter. Each person's sensation of "seeing red" could be entirely different from that of everyone else. We have merely learnt to associate our own particular sensation of "seeing red" with the word "red". We can't even articulate what the sensation of seeing red actually is. Yet another example is the sensation of swallowing. Only I know what my sensation of swallowing is in terms of my particular set of intricate and rapid touch sensations as well as subtle sound sensations. Only you know what your sensation of swallowing is.
The subjective world is a place of personal pleasure, of love, emotions, sadness, memories, smells, sensations, and all the other personal things. It is entirely a necessary thing for each person. But each person's subjective world belongs exclusively to that person. I may open up some of my personal world to some people by telling them how I feel etc., but they will never really appreciate the feelings as I have them. We can empathise with and show compassion for each other but each person's subjective world is beyond the reach of any other.