Four similar things come to mind with this.
1. freezing the lane.
2. pushing the lane.
3. "stopping" the lane
4. understanding minion times
1. freezing lane -- when your opponent has the same or more minions then you, you keep the relative minion count constant to avoid the lane moving, usually "freezing" it just far enough away from your turret so that the minions aren't being hit but it's very difficult for your opponent to cs. You usually want the opponent to have 1-3 extra minions at any given time, as your minions will get there faster, but its possible to do for some time even if they start off as even.
2. pushing lane is when you clear your opponents minion wave, or do a significant amount of damage to them. There are a few benefits to this. At early lvl it can let you get to lvl 2 faster, which depending on your character could be important for a first blood. When your opponent backs it is important you push the wave to their tower so they lose cs/exp (unless your freezing lane and "zoning" them anyways, u can look that up if not familiar with it). Pushing lane also refers to when the minions are naturally pushing (aka, u have more minions than they do, etc). This is important to recognize both in lane and late game, as if a lane is pushing late game you do not need to worry about your tower getting overrun/can focus on team fights, while the other team needs to keep an eye out.
3. "stopping" a lane (my own phrase here), is when you either take some hits or bring a wave off to the side in order to stop them from going into the tower/freezing the lane. The benefit is of course that you can freeze the lane near your turret instead of having it reset. You can look up all of these except number 3/4 and find a lot of guides/info on them.
4. again my own phrase. Depending on when you push lane/are getting pushed/how far minions are in getting to lane can dictate what you can do and how much time you have to do it. For example, if your going for perfect cs, it's important to know that you can steal a wraiths and get back in time without losing any cs from lane. It's also important for recognizing when a lane will reset if you push it. I have not found a guide on that yet but i'm sure one exists. Generally, if the wave is big and/or minions are close, pushing a lane will generally leave it pushed. A common mistake i find low elo people doing in ranked is pushing the lane early but not so much that it goes to the turret. As a result, a gigantic wave builds up mid and the opponent is able to safely farm under the tower while the person who pushed tries to stand nearby simply trying to get exp while the opponent catches up in level. It leaves them very vulnerable to ganks and they lose out on a ton of cs as a result. On the flip side, if you the person who got pushed tries to freeze the lane, they almost always die b/c they take so much dmg from the minion wave.