Ok here goes. This is how CSR is supposed to work however it doesn't always.
Individual Rank Playlists:
It is all about your kills and points at the end of the game. It has nothing to do with K/D spread and wether you win or not. The more kills and points you get, the more likely you are to rank up. If you get a better score and more kills than someone with a higher csr than you, you are very likely to rank up. However if you get less kills and points than someone with a lower csr, you are more likely to rank down.
Team Rank Playlists:
These playlists are all about wether you win or not. Yet again nothing to do with K/D spread. It is also slightly influenced by how much you contributed to the team. i.e getting more flag captures or more points in the hill or with the oddball. If you win in this type of playlist, you are likely to rank up in csr. If you win against someone with a higher csr than you, you are very likely to rank up. However if you lose to someone with a lower csr, you are more likely to rank down.
Hope this helps, just remember it doesn't always work like this. You will have to ask the Halo gods why.
If you still don't understand watch this: