The meaning of "rennen" is "to race/run/spring" and the meaning of "laufen" is " to run/walk/go" 'Gehen' is usually used to indicate going by foot. 'Rennen' is pretty much the same as 'to run'. 'Laufen' however is really a rather strange word. Occasionally it is used as 'to walk', but I would say it's more common as a weaker form of running, more like jogging. For example, when running away from a wild animal you would use rennen, when you run/jog around town to improve your fitness, laufen is more appropriate. Basically: gehen laufen rennen sprinten; Hope this helps!
There seems to be a regional difference in how laufen is used. In the north, it's closer to gehen and in the south it's closer to rennen. I think of laufen as "run" and rennen as "race" (because "racecar" is rennwagen) but Duo doesn't always accept "race" for rennen. I always report that as an error.
In the Stuttgart area in SW Germany (please do not interpret these as rules for standard German, especially the one for "laufen"):
*Gehen is similar to the English word "go", e.g. "wir gehen nächste Woche zu meiner Oma" could be on foot or by car or maybe even by plane. It is just not used in all cases where "go" is used: "Wir fahren mit dem Auto"/"Wir fliegen mit dem Flugzeug"
*Laufen is an all-purpose word which can be walking or running
*Rennen is used for fast running (as fast as you can, e.g. to catch a bus)
*In the local Swabian dialect also the word "springen" is used which means something like "go quickly on foot".
The usage of "laufen" by Swabians often confuses people who are not from that area and would use "gehen" instead.
To "run a show" is an idiomatic expression that will not have a direct translation. To use a modal verb like "können", we can create a sentence like "I can run fast/quickly." = "Ich kann schnell rennen." Bear in mind that when you use a modal verb like können, that modal verb is conjugated and the other verb (rennen, in this case) appears in its infinitive form.
So my understanding of "laufen" is "to walk" and "rennen" is "to run" can someone tell me if i am right or wrong?
gehen is to walk.
rennen is to run
laufen is... either. It can mean "walk" or "run".
In the north of Germany, it's more likely to mean "run", and in the south, more likely to mean "walk", but it can have either meaning anywhere, depending on the context.