I largely rely on the canon explanation of Jump, but visualize it in two ways. To explain the effect of gravity to my players, I use the metaphor of a submarine, having to get to deep water (minial gravitic stresses on local space) to submerge and being forced to surface when the bottom gets shallow (a strong gravity field). To understand Jump Depth (i.e. 1-6) I conceptualize it like a river, with placid current (Jump 1) close to shore and fast moving ones (Jump 6) in the center. It takes more effort to paddle out to the fast flowing current (higher fuel requirements) but the speed gain can be worth it.
One of the additions I made to the jump drive is an internal component termed a jump lattice, essentially a power regulator of sorts. The higher the Jump number the better alignment your lattice must be in accordance to an absolute specification. So a trusty Jump 1 drive is like a hardworking diesel engine that takes a licking and keeps on ticking. It can be almost an inch out of alignment and still function fine. But a highly finiky Jump 6 drive has a alignment requirement within microns of the specification and drives engineers crazy by having to be realigned or "retuned" after every Jump and frequently after combat or atmospheric entry/exit. That's why it's still so infrequently used and so expensive to maintain. In fact the way I work it is that the higher Jump number drives has significantly increasing maintainance requirements. And anything above a Jump 4 can't even use unrefined fuel without assured catastrophic results (even a Jump 4 makes using unrefined fuel chancy). But a Jump 1 can use it for a couple Jumps without a problem.