Embryo transfer can be carried out on any day of development, although most clinics do so on either day 3 or day 5 of development. The primary benefit of growing the embryos in the lab as long as possible is that with each passing day, there is a greater variation in the quality of the embryos, allowing the best to be more easily identified. To better understand this concept, think of embryos like runners in a race.
Imagine that there are 20 runners in this race. At the starting line, they are all at the same place – there are no winners or losers. This is equivalent to day 1 when fertilized eggs all look the same. The runners stay quite close together at the beginning. As the race goes on, the stronger runners stream ahead of the slower ones. Eventually, there is a winner. Running the whole race is equivalent to leaving the embryos until day 5 and choosing the "winning" blastocysts for transfer.
In other words, when there is a large pool of embryos to choose from, letting them develop in the lab until the blastocysts stage at day 5 can help to sort the most desirable embryos from the least desirable, thus allowing for the selection the best embryos to transfer.
Now, what would happen if there were only three runners in the race and you only had to choose the top three? To accomplish this, you do not need to wait until the finish line. In other words, if there are only three embryos in total and you want to transfer three embryos, they can be transferred on any given day. If you end up with the exact number of embryos that you plan on transferring or some embryos clearly stop growing early on, it becomes possible to choose the best embryos for transfer on day 2 or day 3. In fact, they might grow better inside the body than they would if they had been kept in the laboratory incubator; we just don't know for sure.
Hopefully, the race analogy helps you to understand why embryos are transferred at different times.