As with all silicon chips, DRAM uses transistors that consume power when switching between states. This energy is turned into heat, and if you want your computer to perform at its best, it's good to keep that temperature down. The most common way to do that is by using a heat sink or spreader on the RAM.
While these are a holdover from the DDR and DDR2 days of enthusiast memory, they're no longer necessary. These days, most decent RAM sticks run at a low enough voltage to stay cooler than their maximum operating temperatures without any extra cooling. And even when they do get hot, they're usually only a few degrees warmer than bare chips and can be kept under control with proper case airflow.
Besides adding aesthetic appeal, which is always nice, the biggest reason to use heat sinks on RAM is to protect it from thermal damage. If a piece of memory gets too hot, it can fail or cause damage to other parts of your computer. And while it's not likely, any additional protection is a good idea.
The good news is that you can find plenty of different designs for RAM with heat spreaders, from simple silver or black to vibrant colors and even glowing effects. So if you're not interested in protecting your RAM from potential damage, you can still benefit from the aesthetics by picking a design you like. But if you're going to use them, make sure that you buy RAM with a compatible motherboard. Otherwise, it could cause compatibility issues.