For those of you wondering what a custom ROM is, here’s a brief explanation.
A custom ROM is basically an “open-source” modded version of original stock Samsung firmware or built from Android sources. Most custom ROMs include new features otherwise not included with your Galaxy Note 3 such as ability to record calls, customize UI/system, and much more.
Why install custom ROMs on Galaxy Note 3?
There may be many reasons to install custom ROMs on the Galaxy Note 3.
First, you may want to run a clean, lightweight ROM without all the bloatware carriers like to put on. And there may be many apps/features you don’t use with the Note 3. In that case, it may be better to run custom ROMs as they come clean without all the junk.
Second, you may want to turn your Note 3 into a stock “Nexus” phone by installing an AOSP ROM (What is AOSP?). AOSP ROMs contain none of Samsung features yet they will give you the latest Android OS. For example, if Android 4.4 Kit Kat was released tomorrow, you would be able to install Android 4.4 Kit Kat OS using AOSP ROMs in a few days after without waiting for Samsung to update their software (which may take many weeks/months).
For more information, see What is an Android Custom ROM?