Basically, you need to know that the leading strand is synthesized faster and without any breaks, but the lagging strand is synthesized more slowly and in fragments. Both new DNA strands are synthesized by DNA Polymerase going from 3' → 5' direction on the template strand and therefore synthesizing the new strand in the 5' → 3' direction.
If you want to try to understand why that is, here's my best shot:
Disclaimer: "Something about this topic was incredibly hard for me to conceptualize all throughout high school and college. I did not understand why Okazaki fragments formed until I started teaching and HAD to be able to explain it.
Think of DNA polymerase (the enzyme constructing the new strands of DNA) as one of those wind up toys that can only move forward (***see attached pic of yellow smiley face toy***). Like the toy, DNA Polymerase can only move down the template strand of DNA in the 3' → 5' direction (synthesizing the new strand in the 5' → 3' direction). Well, the two strands of DNA that have to be replicated actually run in opposite directions of each other. Therefore, one strand (leading strand) will be replicated relatively quickly and straightforward, while the other strand (lagging strand) will have to be synthesized backwards...but the catch is that just like our little wind-up toy DNA polymerase cannot move backwards. So, instead it must wait for DNA helicase to "unzip" a section of the DNA, and then it will start synthesizing new DNA from the point nearest the DNA helicase in the opposite direction from which DNA helicase is moving. DNA polymerase will eventually get to the beginning of the DNA strand, so it will then detach and reattach at the point nearest to the DNA helicase and start synthesizing another fragment again in the opposite direction from which DNA helicase is moving (until it gets to the start of the first fragment and the process begins again). Think of it as having to pick up our little wind-up toy and move it further along in its journey to the other side of the table because it's facing backwards and keeps walking in the opposite direction that we want it to go.
