Okay, the question you're probably asking is "so what really is the difference between a 3-4 and a 4-3 defense?" After hearing Offerdahl talk about it, and seeing news about the Dolphins running a 3-4 with a rushing LB, its a reasonable question.
Here's some help for you:
In a 3-4, the Nose tackle lines up over center, and his job is to occupy that center. The ends are further outside, and generally will occupy the tackles. That means that the inside linebackers are going to go up against the guards on most plays; on runs the guards are going to come out to take on those linebackers, and on passing plays they will seek to stop the rush from them. The FB will often block one of the outside guys, while the other will go against the tight end.
So, your inside linebackers tangle with the offensive linemen which will wear them down over time. Linebackers aren't the big guys that defensive linemen are.
Why use this scheme? It uses linebacker speed and mobility to an advantage. Often one of the 4 linebackers will rush the passer to create some issues for the offence - the key is to never let them know which one. In the type of defense Miami plans to run, the LB on the left of the defense will likely be the guy to rush most often, hence the need for a hybrid pass rusher to play the position.
The 4-3 move replaces an inside linebacker with a defensive tackle, and they line up - typically - against the guards. The ends move out a little further and take more of an outside rush against the offensive tackles. The middle linebacker will either square off against the center or fullback, but is less likely to rush. The outside linebackers face off against more or less the same players, but their role changes because they need to play pass coverage first. And all the linebackers typically rush the passer infrequently.
Why use this defense? You occupy the offensive line with many players - big bodies - so you can use your linebackers in coverage and to make tackles on runs. But, you have fewer options on who to rush (in general).
And its the coaches who make some adjustments during the game to make - or based on next opponenet - the most of both to control the game on defense.