if one speces is reduced, it must assist another to undergo oxidation by taking electrons from it
so...
species oxidized goes up in charge, loses electrons and is the "reducing agent"
species reduced goes down in charge, gains electrons and is the "oxidizing agent"
************
oxidation and reduction is all about electrons.. and remember they have a -1 charge !
again.. the easiest way to remember this is this..
1) reduction = reduction in charge
2) agents are assistants
*********
as to chlorine.. think of where it came from
1 Cl2 + 2 electrons ----> 2 Cl(-1)
notice that in Cl2.. each Cl has a 0 charge.. why? because the overall Cl2 has a zero charge.. and each Cl atom has exactly the same "electronegativity".. ie exactly the same desire for electrons. So the electron density is split evenly between the Cl's. Same goes for O2, N2, H2, F2, etc.. O in O2 has charge = 0, N in N2 has charge = 0..etc
so..
Cl goes from 0 to -1 and was "reduced" by gaining an electron
if Cl went from -1 to 0 it would be oxidized and it would have given up an electron.. but it doesn't really like to do that because it has a full out octet and is happy.
*************
bleach..
NaClO..
Cl is +1
it reduced to Cl -1 in certain reactions.. (because Cl has a high electronegativity) and is therefore an oxidizing agent.. and gains electrons
*************