I come from a print & web background and only recently started doing work for motion/video so I'll do my best to help and give advice.
I have a gigantic library of reference images — stuff I've found on Behance, Dribbble, Flickr, Instagram, Pinterest, Vimeo, you name it. My reference folder is currently 11GB and dates back to 2005. I keep it all on Dropbox so that I can access the references from anywhere. When time allows, I will spend up to an entire day just gathering reference. I like to place them in an Indesign file in a nice little grid and print it out so I can tape it on the wall of my cubicle for the duration of the project. Sometimes, I have 3 pages on the wall. Having references is a huge thing for me. Artists like GMUNK have vast amounts of reference (he uses Pinterest) and they go to it on a regular basis.
In regards to assets, I store it all on Dropbox as well. I've got loads of footage like pre-rendered particle animations, environmental images (snow, rain, dust etc.,), lens flares, light leaks just about anything you can think of I try to collect. I do the same for still images. Over the years I've made my own textures (once I get a decent camera I hope to make my own footage too). I keep this stuff handy with a shortcut on my Finder sidebar.
For example, on this board (that is on hold for the summer so I've yet to finsh), I brought in video footage of light leaks and ink bleeds (so that I know I can use the actual footage to pull of the effect in animation when the time comes). I also used a few still images for texture. Thankfully it's still a work in progress because I've questioned numerous times "why did I use the ink bleed? What does it have to do with Hockey, let alone the New York Rangers?". Unfortunately I've yet to come up with an answer other than "I like the way it looks and it serves as a transition to the next frame" however like Binky said, you have to keep questioning why you're adding things. The background (the roof of Madison Square Garden) is an iconic feature of the arena the Rangers play at so including this felt right but I feel that I can take this even further and use the roof of the building as a core element, possibly projection mapping? The scratched textures were brought in to provide a distressed/old feel since most of the footage/imagery is from the past and this is about the "history" of the team. It also lends itself to the texture of the ice that the players skated on without going cliché and slapping an ice texture on the canvas.
The point here is that you need to keep experimenting and as much as I dislike the term — playing, with your concept/idea. Sometimes you'll push too far and you'll realize that you added too much unnecessary fluff but thankfully, you have the ability to peel back.
Building off of what Binky/Carey said, I think that understanding your subject matter inside and out makes a huge difference. George Lois (old school Art Director form the 60's that did the famous Esquire covers) said that if he doesn't come up with an idea in 20-30 minutes, then there is something he doesn't understand about the subject. He went on to say that if you're cultured and understand different things like language, art, music, dance etc., that you will find that ideas come easier. I'm paraphrasing here but I find that it holds true in all areas of design.
Another thing that I find makes a huge difference in "good designers" and "mediocre designers" is collaboration and socialization. I consider myself in between "good" and "mediocre" but when I stopped hanging out around my peers is when I started falling apart. Getting back into "the design scene" and not shutting myself away from the community was a huge detriment to my career development. Talking to and hanging out with other artists, designers, animators, editors, illustrators et al will only further your development. Thankfully social media has made it much easier than it was in the early 2000's where all we had was AIM and Message Boards.
TLDR: Collect references, collect assets, experiment with your work, understand your subject matter, collaborate and socialize