Water is a great solvent. It’s neutral and doesn’t provide any strong positive or negative effects. It just helps components to mix better and to transport active components.
Butylene Glycol is a very popular synthetic alcohol. It helps the product to absorb deeper and faster. It is also a solvent for other ingredients. As for the skin benefits, it helps to attract water and helps to make the skin softer.
Unlike many other “Glycols”, it is not harmful and that's why it is used in many products. It was approved by US FDA and US EPA for usage.
Hexylene Glycol is mostly used for formulation purposes. It’s a good surfactant, emulsifier, and viscosity-reducing agent. It maintains the density of the formulation of the product preventing it from separating. It also makes the product feel better.
PEG-40 Hydrogenated Castor Oil helps ingredients to mix better. It has nice cleansing activity helping to remove sebum and dirt from the surface of your skin. It's also responsible for making soft foam in soaps, shower gels, etc. Despite it having "PEG" in the title, it's considered to be safe.