What does "bxa1=Q" mean? I have a PGN file with the following move in it:


  
  fxe5 bxa1=Q
  


I understand the equals sign represents a draw offer, but what does "=Q" mean?
I would read it as "Pawn takes something on a1 and promotes to a Queen".

Strictly according to the Laws of Chess the = sign should not be there (see article C.11).


  C.11
  In the case of the promotion of a pawn, the actual pawn move is indicated, followed immediately by the abbreviation of the new piece. Examples: d8Q, exf8N, b1B, g1R.


However this is a PGN file, which has its own rules for game notation and it uses the = sign for pawn promotion (see paragraph 3 of article 8.2.3.3 in the PGN standard specification also available here, which should probably be the official reference). 


  [...]. Pawn promotions are denoted by the equal sign "=" immediately following the destination square with a promoted piece letter (indicating one of knight, bishop, rook, or queen) immediately following the equal sign. As above, the piece letter is in uppercase.


Draw data is handled in so-called  EPD records for describing chess positions, using verbose opcodes like draw_offer.  Although it isn't included in PGN proper, specifics are included in articles 16.2.5.8 - 16.2.5.11 of the standard.