So DNA replication occurs differently on the different strands of DNA. Remember, we're dealing with the double helix, so there are two strands of DNA. It has to be unwound and replicated in order to have the two new strands of DNA. We say that there are two template strands: there's the leading strand and the lagging strand, and these are replicated differently.
The leading strand is replicated continuously, adding nucleotides from 5' to 3'. This is the orientation on the new strand, the strand that's being synthesized. DNA is always synthesized from 5' to 3'. On the lagging strand, it proceeds discontinuously, adding nucleotides from 5' to 3' as well.
If the new synthesized strand is being made from 5' to 3', that means that the template strand, what is being copied, is read by the enzyme from 3' to 5'. This is commonly a question on a test or a quiz, and people get confused because they are not sure which strand they are talking about. So, synthesis happens from 5' to 3', which is talking about the new strand that's being made. Whereas, the reading happens from 3' to 5', and that's on the template strand.
DNA is being unwound here. If we consider that only a particular part was unwound, for the leading strand, that works because it can start replicating this way, right on a 3' template, and it starts synthesizing from 5' on a new strand. As the DNA unwinds, it just keeps on replicating and it will replicate all the way to the end, and that's the leading strand.
The lagging strand is different because it has to be read and synthesized in the same way, from 5' to 3'. But in this case, on the lagging strand, the DNA is anti-parallel. Meaning that the 5' is on the template, and the 3' is here. So it has to be replicated backwards. DNA is still being unwound from here, but it can't start and go this way. It has to wait until the DNA is unwound to a certain point, say here, where it starts replicating this way. By the time it's replicated this, some more DNA has been unwound, and it can start here, and replicas till it gets to its other previous fragment.
As the DNA unwinds, it can keep going, but it does this discontinuously as the DNA unwinds because not all the DNA is unwound. This, on the leading strand, just sort of travels along with the unwinding enzyme, which we'll talk about, until it gets to the end. But this one, because it goes backwards essentially, has to wait for this unwinding to occur so it can start and synthesize in this 5' to 3' manner.
So the leading strand and the lagging strand are different because the orientation of each template is anti-parallel. One has to go one direction in the leading strand, and the lagging strand has to replicate in the other direction. If you ever get confused about the direction everything is moving in, please feel free to come back to this image because there's always a question about the direction things are occurring in, and people get so confused. They usually miss the question, not because they don't know, but because they're just unsure whether what's being synthesized is in what direction. But I feel like this image is fairly clear, and is always a good resource to go back to. So with that, let's now move on.