So ships have emissions (generally speaking, heat). Higher grade sensors allow you to get a target box on them sooner, and thus, lock on for scanning or gimbal/turret attack. Cooler ships, like Diamondbacks, can be trickier to get a lock on because they run so efficient. Likewise, "silent running" mode reduces your emissions (heat, by building up and storing it within the ship -- ie: not venting it to space) so that you become "invisible" to standard sensors. You'll note if your target dumps a heatsink, you will often lose lock on them. This is why.
Sensors can pickup blips in all directions, but you can only "scan" and thus lock on to targets within an angle/arc (facing them within 25-30* usually).
Lightweight engineering lowers the weight of the module, increasing thrust/jump distance. This generally comes at the cost of nerfing your emission range or scan angle. Integrity is often lowered for that kind of engineering as well (ie: the module breaks quicker in combat).
In other words, you can lock on from further away and at wider angles. Wider angles is better for ships that turn poorly and fight closer to a target. Long range scans, the angle is less important because you can keep them inside it because they are... further away.
Agile ships wouldn't care so much about scan angle because they can overtake whatever they are scanning.
I find both range and angle to be marginal and often opt for lightweight because jumping and thrust are more important to me. If you opt for fixed weapons it's not quite as important either, just for that initial scan. It's really a preference thing -- im not sure the values altered are all that significant, but I guess it depends if you fly a quick ship or a slow one, or spend a lot of time target scanning. If weight is not much of an issue for you (bigger ship), lightweight probably won't help all that much. Lighter ships take big hits on extra tonnage so lightweight helps them tremendously.
