A good pair of motorcycle boots don't begin working in a crash. They've been keeping the heat of a hot exhaust away from your ankles. They've been deflecting debris and wildlife from your shins. They've kept your feet comfortable and responsive for operating the foot controls, all while resisting the British weather as it tries to turn your feet into cold, soggy logs. As with all motorcycle gear, it's there to make the experience better, not spoil the fun.
If you're just getting into motorcycling, you might be tempted to put on a sturdy pair of normal boots and hit the road. Hey, it's better than a pair of flip-flops. But motorcycle boots have great features to make motorcycling safer and more comfortable, such as pads near the big toe to prevent wear from the gear shifter, or anti-slip soles so that you don't lose composure while dismounting - even on an oily surface like a petrol station forecourt.
Your feet could impact an obstacle, run along the asphalt or even get trapped underneath your bike in an accident. A motorcycle boot is made of thick, strong leather or something similar that will resist abrasion and minor impacts. Solid shin plates, heel cups, ankle guards and solid toe caps stop these areas being crushed. The overall design will resist twisting to protect your ankle.
Shorter boots that only just come above the ankle can be more comfortable, especially if you're not taking a spare pair of shoes to the office. However, they do pay a large price with regards to safety. A shorter boot simply cannot provide the same support to the ankle, and does nothing for the shins. We see how important this is if we look at some statistics:
39.6% of foot injuries in a motorcycle accident are to the talar, the bone between the heel and the knobbly bits 
41.5% of motorcyclists with foot injuries also had a broken ankle 
28.3% of motorcyclists with foot injuries also had a fractured tibia (shinbone) 
The comfort/safety tradeoff decision is one that only you can make for yourself. Even if we set crash protection aside though, it's surprising how annoying a bumblebee strike can be on an unprotected shin at motorway speeds.
Even a budget pair of motorcycle boots will be better than normal boots, but if you're enjoying a specific type of riding, you can pick up a pair with features to improve your experience.
Racing boots have even greater protection, as they're designed to deal with incidents at much higher speeds. They also usually have toe sliders - plastic strips running along the front of the toes that are designed to grind against the asphalt through a corner. They're often ventilated to keep them comfortable through all of the excess armour.
Off-road/Adventure boots have a reinforced arch so that they're comfortable standing on the footpegs for long periods. They also have more aggressive treads on the soles for traction on gravel and muddy green lanes.
You can get casual-style boots that look like a normal pair of boots or even sneakers. You just need to make sure they offer all of the protection you're looking for.
The most popular way to fasten motorcycle boots is with tried-and-tested laces. They remain popular because they do a great job and make it quick to get the boots off. However they can come undone while riding and when they do, you could have laces flitting around near chains and belts and spokes.
Modern boots often come with zips which are quicker than laces. They tend not to come down while riding and there's nothing to get caught up in moving parts. On the other hand, they can be temperamental. We've all had to contend with a broken zip at some point.
Clasps are another quick, durable option that are particularly popular on off-road or adventure style boots.
Many manufacturers will use one or a combination of the above on their products, along with velcro straps or buckles to keep laces or the zip tags from flapping around.
A recent option is the BOA system that's been used for snowboarding footwear for a while. These replace the laces with a stainless steel cable, and add a small dial for tightening them.
As with all of your gear, you'll have to make a choice depending on what you're riding and where you're riding it, as well as what you like the look of and how it fits. Boots should be a bit snug and will relax over time. Your best bet is to pick a few pairs that have the protection and features you need, and then try some on.