Unconditioned Response -
An original or normal reflex to a stimulus, as opposed to a conditioned response which is learned behaviour. A dog will normally salivate when it sees food and so this is an unconditioned response but with training the dog can be made to salivate in response to a bell ringing, this is a conditioned response.
Unconscious Mind -
The unconscious mind is a collective term which covers all the mental processes that are operating outside of immediate consciousness awareness. This has been likened to the iceberg metaphor where consciousness is represented by the one seventh of the berg which stands above the waterline. The seven eighth's of the berg below the waterline representing the unconscious mind. Another analogy is the eating process, where eating represents the conscious processes while digestion, assimilation are unconscious. There are areas where conscious and  unconscious processes over lap. Breathing is such an example: most of the time we are unaware (unconscious) of our breathing, especially during sleep, but it is possible to consciously intercede and modify our breathing patterns. So it can be seen that we have unconscious processes that are so 'deep' that we are never consciously aware of them, while other unconscious processes are only unconscious because they are not 'in' consciousness, or temporarily forgotten.

A good example of an unconscious process, as something that continues even though we are no longer consciously aware of it, is afforded by the memory.
You will no doubt have had the experience of trying to remember a particular name or fact but found that you were unable to do so. So you continue about your normal affairs and might think, or be consciously aware, of many other things when the name or fact suddenly 'pops' into your mind (consciousness), proving that a process has taken place (unconscious search) beyond your conscious awareness (unconscious). 

It is not clear which faculty decides whether a process will be unconscious or consciously available to us but it does seem that a 'need to know' rule applies. Processes that we no longer need to know about (they are not a danger to us, or we have become so conditioned to them that the process can be carried out unconsciously) do gradually pass into the unconscious. Yet it seems that some non conscious faculty, or element is always vigilant. This is evident at a large gathering where you are struggling to make yourself heard and all you might consciously hear is a babble of background noise from the crowd, but if someone mentions your name you will suddenly become very conscious of it. Likewise a mother (until she has become conditioned otherwise) will awaken from deep sleep if her baby murmurs or moves.

Perhaps the most important fact from a psychological / hypnotheraputic point of view is that the unconscious mind is the repository of memory. Thus therapy is usually a matter of investigating or modifying or bringing into consciousness some causal dynamic (usually trauma or false learning) which has become buried in the unconscious mind. 
Psychoanalytic theory posits that there is some form of psychic filter which keeps 'unfacable' memories connected with unpleasant events away from consciousness (repressed), hence the difficulty involved in recovering them. 
It may be that there is no such 'filter' but repression is simply a continuation of the minds natural process of 'deconditioning' memories that are not often used. If you require a particular fact (memory) every day it will become conditioned to appearing in consciousness and will be readily available for recall. In other words it is valued as important. A traumatic event is unpleasant an unless repeatedly bringing it to consciousness brings benefits it will naturally be 'forgotten' or deconditioned from consciousness. 
Then there is the 'state dependent' theory, that works on the theory that memories do not exist in isolation but are a composite of external and internal states. With this theory, memories are recoverable while the individual is in, or near to, the external or internal state that they were in during the original learning experience. As an extreme example a person who was heavily intoxicated the previous night might have no memory of events that took place then, but if the individual returns to the intoxicated state them the memories can become available. Similarly dreams are easily forgotten upon awakening (because the state has changed from sleep to wakefulness) and a way to retrieve them is to return the body to the exact position it was in on awakening. From this theory it can be seen that memories might not actually be screened by a filter but may be unavailable because of the difference between the physical and mental state at the present moment and the time at which the event occurred.

Is there a simpler answer?
The unconscious could be said to be everything that we are, but are not aware of.