@Guaire,
Choice, Free Choice or Free will is a linguistic term describing a situation where "A person would have the option to make decision A or B in given situation X." [We know that there are all sorts of constraints effecting our choice but we still feel we have some level of freedom to choose.]
The concept of free will is very important since responsibility can only be meaningful if there is free choice. [There is no point punishing a murderer if he had no choice in the affair - no free will no responsibility.]
Free will is not a theory, not a belief, it is a linguistic phrase [in the absence of determinism] describing a situation which appears to be free, therefore it needn't to be proved. [It is like atheist's useless attempt proving the non-existence of God - it is not possible - all he needs to do is wait the claimer of God to prove the existence of the deity.]
The term "Determinism" implies the existence of a "Determiner". If the defender of the Determinism who is able to identify precisely who the Determiner is and what he/she/it has determined and even demonstrate his claim in a controlled experiment then he will have a plausible argument. [But nobody has ever succeeded it.]