How to keep track of all things you are carrying in the luggage and where they are? mentions packing cubes and amenity kits. Can somebody explain or/and elaborate about what these are and how they help a traveler packing clothes?
A packing cube is a zippered bag (generally more of a rectangular cuboid than a cube if we want to get into it) for storing clothes and other supplies when traveling. One popular manufacturer is Eagle Creek; I have some Spacepack ones (which I don't think I paid nearly that much for) as well; those have a nice two-sided design so you can separate clean and dirty. A similar product is available in the form of packing folders, which work well for dress shirts, blazers, and slacks. Since they're roughly rectangular, you can pack several up together in a suitcase with minimal wasted space, filling in shoes, sweaters, and other items to occupy any gaps.
The idea is that you can fill them with neatly folded clothes (or tightly rolled up clothes if that takes less space) and other items (such as electronics, they make padded ones), then put the cubes into your bag. This avoids having a bag full of loose disorganized clothes, helping you find what you need and keeping it neat. I'll usually organize things into different cubes based on type: socks and underwear in one, t-shirts in another, button-down shirts and pants in a folder. Unpacking is as simple as pulling out the cubes and packing just involves putting the cubes back in your bag.
Amenity kits are small zippered bags often given by airlines to (usually international) first and business class passengers containing various travel supplies, such as a sleep mask, toothbrush and toothpaste, earplugs, socks, perhaps a comb and a small container of hand lotion, etc... The supplies are useful, but the bags they come in are also handy toiletry bags for future trips. If you don't happen to have your own collection of premium cabin amenity bags, you can buy a toiletry bag of your preferred design, which is what most people do.