According to Stanford University's Encyclopedia of Philosophy, determinism suggests that every event or action can be explained by examining the causal chain leading to it. Compatibilism --as opposed to "hard-determinism" -- recognize's man's free choices, as long as his own will is one of the steps in the causal chain. For example, a man walking down the road and smelling a hot-dog makes a free choice to buy one. However, it is the chain of events (the vendor sold hot dogs on a specific street and specific hours and the man has a reason to walk down that particular road) that allowed the man to come up with a dilemma (buy or not buy) and make a choice.
Determinism suggests that man's progress in life is like a river: it is free to flow freely, but only within its banks. People are influenced by external factors, that make it rather improbable to choose or act otherwise. For instance, a young man is thinking to move to the city for a better life, because work on the farm is hard. What he has to take into consideration however is also the savings he has, his relationship with family and friends, breaking the family's traditional occupation path, as well as the cost of living in the city and even the bus fare. All these factors can lead to a decision different than the man's ideal choice.
On the other hand, free will is the acknowledgment of people's ability to make their own personal decisions. The notion is pivotal, as accepting the existence of free will means recognizing free action and with it moral responsibility. In addition, uninfluenced choice is a basic element of liberty, which philosopher David Hume defined as "power of acting or of not acting, according to the determination of the will."
According to Trinity University, "action is free if and only if its cause is internal to the agent ... caused by the agent's beliefs and desires." However, these beliefs and desires may as well be the result of brainwashing (beliefs forced by someone else) or addiction (a regular smoker does not decide freely if he wants to smoke or not). In addition, coercion is also a factor affecting free will, for example a threat or a reward can lead the person to a certain decision, while lying (form an opinion based on false data) can also manipulate a person's actions.