Essentially imagine an assembly line in a factory. Imagine that, as each item passes through the assembly line, it will go to employee 1, then employee 2, on up to employee 5. After employee 5 is done with it, the item is finished and is ready to be packaged. Thus all five employees can be working on different items at the same time and not having to just wait around on each other. Unlike most assembly lines though, every single time employee 1 starts working on a new item, it's potentially a new type of item - not just the same type over and over.
Well, for whatever weird and imaginative reason, imagine the manager is standing at the very end of the assembly line. And he has a list saying, "Make this item first. Then make that type of item. Then that type of item." And so on. As he sees employee 5 finish each item and move on to the next, the manager then tells employee 1 which type of item to start working on, looking at where they are in the list at that time.
Now let's say there's a point in that list - that "sequence of computer instructions" - where it says, "Now start making a coffee cup. If it's nighttime when you finish making the cup, then start making a frozen dinner. If it's daytime, then start making a bag of coffee grounds." This is your if statement. Since the manager, in this kind of fake example, doesn't really know what time of day it's going to be until he actually sees the cup after it's finished, he could just wait until that time to call out the next item to make - either a frozen dinner or some coffee grounds.
The problem there is that if waits until the very last second like that - which he has to wait until to be absolutely sure what time of day it'll be when the cup is finished, and thus what the next item's going to be - then workers 1-4 are not going to be working on anything at all until worker 5 is finished. That completely defeats the purpose of an assembly line! So the manager takes a guess. The factory is open 7 hours in the day and only 1 hour at night. So it is much more likely that the cup will be finished in the daytime, thus warranting the coffee grounds.
So as soon as employee 2 starts working on the coffee cup, the manager calls out the coffee grounds to the employee 1. Then the assembly line just keeps moving along like it had been, until employee 5 is finished with the cup. At that time the manager finally sees what time of day it is. If it's daytime, that's great! If it's nighttime, everything started on after that coffee cup must be thrown away, and the frozen dinner must be started on. ...So essentially branch prediction is where the manager temporarily ventures a guess like that, and the line moves along faster when he's right.
Pseudo-Edit:
It is largely hardware-related. The main search phrase would probably be "computer pipeline cpu". But the list of instructions is already made up - it's just that that list of instructions has branches within it; it's not always 1, 2, 3, etc. But as stage 5 of the pipeline is finishing up instruction 10, stage 1 can already be working on instruction 14. Usually computer instructions can be broken up like that and worked on in segments. If stages 1-n are all working on something at the same time, and nothing gets trashed later, that's just faster than finishing one before starting another.