It makes more sense if i do this: divide the top equation by two:
1/2 Cl2 + e- ----> Cl-
Forget about the half in front of the Cl, but what basically happened was that you had a diatomic molecule of chlorine (2 atoms) and it gained 1 electron from the bromine (the bromine oxidised, i'll get to that after), causing a Cl-, as now it has an excess of one electron. Thus it went through reduction.
Now with that in mind, if you go back to the original equation, the diatomic molecule gained 2 electrons, causing the each Cl in the molecule to gain one electron each. This coincided with the 2 Cl ions that were created (they weren't actually created, but actually split apart from from the diatomic molecule after the reduction reaction)
Same principle applies to the second equation, we had 2 bromine ions, each with an excess of one electron (hence together they have two electrons in excess). They then oxidised (lose/donated) their electrons to the chlorine, and then joined together to form the diatomic molecule
For redox equations, it's all about looking at them logically. In reduction equations, the species goes from being a neutral atom to becoming an anion. To become an anion, the atom must gain the electrons first, and then the product becomes an ion. Hence the atom + electron ---> anion
For oxidation, the ion becomes an atom. For it to become an atom, the ion must lose electrons. So if you write:
ion - electron ----> atom and move the electron to the otherside, you get ion----> atom + electron