On a nice sunny day there's no reason why you shouldn't slop about town in your shorts and flip-flops - no special clothing needed at all! But once it starts getting to be winter, you get to a point where a few bits of well thought out fabric will keep you warm and dry. There's no need to rush out and buy everything at once though - add layers here and there as the nights draw in.
Cycling can still be comfortable, even if it's cold wet and dark out there. While ordinary clothing is often fine, cycling-specific clothing makes your life easier and more pleasant for a number of reasons.
The cut is more comfortable, as it takes into account the strange position. Cycling tops require lower backs, because you are leaning forward, and sleeves need to be extra long because your arms are stretched out. Shorts and leggings need to come up high, to keep your kidneys warm. Legs need to be stretchy or baggy, so your knees can move.
Breathable clothing keeps you dry from the inside. Waterproof clothing keeps you dry from the outside.
Showerproof and rainproof clothing will not keep you as dry for as long as waterproof clothing. Mostly showers should be assumed to last about twenty minutes.
Bright colours can make you more visible, although not necessarily more attractive.
Windproof materials are warmer. Wind chills you, especially if you are wet. As you cycle, you create your own wind.
Some fabrics dry relatively quickly. This is useful, as you may have to put the same clothes on to cycle home after work.
Normal clothes can suffer badly when used regularly for cycling, especially shoes. It's more economical to buy cycling-specific clothing, and not destroy your normal clothes, if you cycle a lot.
A Fabric Glossary:
Gore-Tex: this fabric is 100% waterproof, breathable and windproof. It is good value for money, although relatively expensive. Clothes made of Gore-Tex are very warm, as the heat created by your body when cycling cannot easily escape. So you don't usually need as many clothes underneath (too many bulky layers also affect breathability). Gore-Tex fabrics are guaranteed to be breathable, wind and waterproof , although this does not include wear and tear, or abuse. Gore-Tex can be washed in your machine using Grangers' fabric wash. The outer layer of waterproofing can be reactivated by tumble drying the garment at a warm setting.
Lycra: life on earth without lycra is impossible to imagine. Different weights are available, thicker lycra is more comfortable, more durable, blocks more wind, and is more expensive. Cycling shorts, leggings and bib tights are usually lycra based. More expensive shorts and leggings are usually made with wicking fabrics increasing their comfort.
Fleece: For cycling fleeces are fantastic insulating layers, and will keep you very warm even when wet, although a windproof layer over the top cuts the wind chill factor. Stretchy close fitting fleece shirts and leggings are ideal since they dont flap about, and trap a layer of warm air next to your skin.