I agree with Tom. You should forget about the word 'proffer'. It is not used in everyday modern English. Sometimes dictionaries do more harm than good.

The dictionary gave the definition of "proffer" as " to offer", so I can see why you're a bit confused. ;) "Offer" is a very, very common word. "Proffer" is not a common word at all. It has a specific meaning in the legal system that is not generally understood by your average fluent speaker of English. To use it to generally mean "offer" in American English is anachronistic - you'll sound like you're trying to talk like Shakespeare. I would avoid its use.

thank you to all

I disagree that proffer is anachronistic. Without looking it up (not that difficult), I suggest it conveys the action of offering e.g. by holding the offering or indicating it physically e.g. I proffered a candy. It strengthens the act of offering.

See: http://dictionary.reference.com/browse/proffer It might look like they are synonyms, but the meanings of 'proffer' seem to be a subset of the meanings of 'offer'. 'Proffer' is more specific. To 'proffer' something is to 'bring it forward (for approval)'. This usually means something in your possession or under your control. You're putting something up for judgment. But you can 'offer' almost anything -- including intangibles and things you don't possess/control, such as future things. You can offer actions and promises, but these aren't things you 'proffer'. Both words come from the same Latin root, just with different prefixes. For more information, see this discussion: http://ask.metafilter.com/6628/Whats-the-difference-between-the-words-proffer-and-offer