If you're the type of person who likes to master a hobby within months - or even weeks - of picking it up, Brazilian jiu jitsu might not be for you. In fact, jiu jitsu is not something that can be learned so easily. Additionally, it quickly becomes more than just a hobby... it becomes a lifestyle. For the majority of practitioners who make it past blue belt, it's as integral to their daily routine as brushing their teeth.
BJJ is an activity that requires knowledge and practice, so obviously one might ask how long it takes to get a proper understanding of jiu jitsu. However, this is not an easy question to answer.
First of all, obtaining an "understanding" of BJJ is quite relative. The casual observer can gain enough of an understanding of jiu jitsu to know what a sweep, pass, arm bar and choke looks like. But when it comes to understanding the intricacies of a particular sweep, or how one position connects to another, then to another... that takes years of practice and dedicated implementation. For many, obtaining the coveted black belt can take anywhere from six to 15 (or more) years. Even then, many a brand new black belt has been known to say that their real journey of learning the gentle art had just begun!
For those who don't shy away from the long haul, getting a sufficient understanding of jiu jitsu is dependent on 1) how you define an "understanding" and 2) how you learn. I can't address your answer to number 1, but I can give you some tips regarding your number 2:
Be Consistent - An understanding of jiu jitsu - of anything really - requires the cumulation of endless hours of practice. However, if those endless hours are piece meal and inconsistent, you can be guaranteed to have a long, slow journey toward your next belt. Being consistent allows you to easily build off of the previous sessions and build a strong foundation for the next session, without having to go back and review something that you had forgotten because you took a few weeks off.
Identify Your Learning Style - Not everyone learns the same. While jiu jitsu is a very hands-on practice, recognizing how you learn will allow you to modify your individual practice to favor that learning style or supplement your in-class instruction with something that enables you to learn the techniques more easily.
Study - As much as you'd like to - especially after you've gotten the "jiu jitsu bug" - you can't live on the mat. There's only so much hands-on training that your body can take before your overstrain yourself. So studying is indispensable to your journey. Luckily for you, many high-level professors and academy owners offer online websites full of video instructionals. And of course, there's also YouTube.
Wherever your journey takes you, and however long it takes, know that your journey is yours and yours alone.
Train on. Oss.