Riot gives you a new provisional MMR. We conjecture that provisional MMR is equal to (your MMR + 1200) / 2; with 1200 being the server average MMR, somewhere in the silver band.
You then play 10 games against opponents around your provisional MMR. Based on your results, you are assigned to a division that is, on average, about three divisions lower than your expected true rating. If you go 10-0 you'll end up in about the same division your provisional MMR was in, while if you go 0-10 you will end up 5-6 divisions lower.
Based on the information you gave me, I estimate that you ended last season in silver 4. Neither lolking nor op.gg have a feature for looking up previous season rankings, so I wasn't able to independently verify that guess.
I can report my personal experience -- I was in D5 to end last season, went 4-6 in placements, and was placed in P3. I played some games over the weekend and acquired 55 LP for winning 50% of games, so clearly my MMR is higher than my current divisional placement by a fair bit.