The 5 skandhas, also known as the 5 aggregates or go-un (五蘊) in Japanese are basically the 5 gateways to our existence. We experience the world through these 5 concepts and they are the reason we are disconnected to our true Buddha-nature and feel our individuality.
In Buddhism, it is understood that we are not separate from the rest of the creation. We are part of it and it is part of us. We are a whole. The five skandhas are what gives us the illusion of separateness as they give us our sense of individuality.
Form is the first skandha. It is the physical world as we perceive it, classify it and experience it. It consists of the 6 senses we use to perceive and classify the world (touch, smell, sight, smell, hearing and thought) and the four elements of the earth, air, water and fire.
All classifications of the world are included in this skandha: feminity, masculinity, weight, height, shape, movement, etc.
The second skandha is sensation, often time called feeling. This later is misguiding though as it could mean a mix of any of the other skandhas. Sensations are the judgment we pass on a perception we gain through the experience of the 6 senses. This judgment, be it pleasant, unpleasant or neutral (the three modes) will determine our future interactions with that sensation. This leads to craving of the pleasant sensations and rejection of the unpleasant one. This in turn leads to suffering.
The third one is perception but it could be better understood as conception or discrimination. It is to mentally recognize the meaning of a form or to register the absence of recognition.
Mental formations are the way our brain arranges the information it gathers through the different senses and perception. They will create our personality when they become habits and character.
This last skandha is like the master. Consciousness is like the coach who allows us to coordinate the team. Through consciousness, we perceive our separateness from the surrounding environment and we process the other aggregates to form a streaming series of thoughts. What choices we make, what decision we take are all a process of consciousness. This is what animates our body. It is the life force driving the vehicle we are lodging in.
The five aggregates are part of why we are suffering. They give us the illusion of individuality and keep us from reaching our full potential of Buddhahood. They are like doors locking us in a cell. When we are able to transcend these, we will attain enlightenment and Nirvana, thus ending the cycle of rebirth and suffering.