Well amongst the obvious, the more flexibility you have, the more fluid your movements can and will be. Flexibility is the length of a muscle where as mobility is how a joint moves, however they go hand in hand. Mobility allows for proper hinging, such as bending down to get something or not developing injuries with every day tasks. If your body has a limitation in mobility, it won't function properly.
1. Stretch- A no brainer however, if you're already super flexible, this is not something you should be doing much of. For example, I am hyper mobile, the technical term for super flexible. My ligaments are so elongated, that my joints aren't tight, they're unstable. So I can do a split like it's nothing, but squatting is hard because my hips want to just do whatever they want! Stretch if you cannot reach your toes, ease up on stretching if you're head goes to your knees!
2. Foam Roll- If you're an avid reader of my site, I wrote an article previously all about foam rolling and how it benefits you. Quick synapses, if you foam roll, you can loosen up tight fascia, (muscle tissue) allow for a rejuvenation of the muscle, a type of reset. It's like unraveling a tight shoe lace.
3. Drills- There are several mobility drills that you can do for all different joints. A good site to use would be MobilityWOD. This is an sorts performance accredited site, full of fitness experts. Drills such as static lunges, band dynamic stretching or behind the neck band pull apart.