In a peer review system, what does "accepted for first look" mean for a submission? As the title puts it, what is the real meaning of this stage of a peer reviewing process and how are the odds for having a submitted paper accepted change if it's accepted for this stage? (Does it mean anything other than the editors decided not to reject it from the start?)
"First look" is a stage in the ScholarOne Manuscripts (S1M) system used by many journals. The First look stage means that your manuscript, after an "Accept" decision is scrutinized to see if it adheres to journal standards (a.k. Instruction for authors) and that figures are of sufficient quality (resolution for bitmaps). The journal editor(s) handle(s) this stage. Your paper may be returned to you to fix specific formatting problems BUT NOT changing the content. See S1M pdf

So "First look" is not a general name for a stage but is specific to S1M. Other systems or journals may of course be using such a term for other purposes but it is not a general publishing term. The stage it represent will, however be found in all journals.