I am silver one with 430+ hours and 85 wins (IKR). And I have just recently looked up how many wins it takes to rank up from silver one. It said 3-4. I won 5 games in a row and still haven't ranked up.
CS:GO ranking system has not been figured out completely and never will be if Valve doesn't reveal it themselves. However, at lower ranks one should usually rank up with 3-5 wins, at higher levels the number of matches needed to win also gets a bit higher.
The factors that are estimated to matter are following:
3. Round wins
4. The rank of your enemies according to you
The amount of 'rank-points' you recieve each match is always different, unless you play with the exact same teams, get the exact same amount of kills and MVP's and none of you have ranked up.
The more kills you have, the more rank-points you get. Same goes to the MVP's, so you should always want to plant/defuse the bomb or get most eliminations.
However, if you happen to be Silver 1 with Global Elite teammates and the enemies have a team of 5 Supremes, for example, if you have the most kills and MVP's and you win 16-0 you would probably rank up instantly, if not many ranks at once.
The same goes the other way, if you lose rounds to a lower rank you lose more rank-points, if you lose rounds to a higher rank you lose less rank-points.
Since kills and MVP's (you can only get an MVP if your team wins the round) count, it really does matter a lot if you lose 14-16 or 1-16. You should never give up and have the 'I've lost the match anyway, what is there to lose?' attitude, because each kill or MVP could save you from ranking down.
Your case was most likely that you lost a number of matches before (and lost rank-points), then won the games either close (14-16) and/or you didn't get enough kills/MVP's.