Technical analysis is the study of past price patterns to improve an estimate about likely future price/volume movements. Although technical analysis techniques differ by analyst, they generally involve looking for things like trend lines, support/resistance levels, momentum indicators, breadth indicators, oscillators, moving averages and MACD, bollinger bands, average true range, etc… Sometimes it also involves things like chart patterns (cup and handle/ head and shoulders, etc.)
By today’s standards of analysis it is not especially “technical” but historically these methods were considered technical before the advent of significant computing power, because computing many of these things by hand was considered highly technical work (which, without computers, it probably was). Today, quantitative analysis has taken the lead in the application of complex formulas, but tends not to do a lot of chart-type work, except in CTA strategies, which have also suffered a lot lately, and some limited use of momentum indicators.
Most mutual funds and long-short shops tend to be fundamental analysts, which means they tend to look at the fundamentals of the business, make projections of future profits, then discount them to the present to come up with a price or price multiple to determine whether things are overpriced or underpriced relative to the risks of those profits actually materializing. A large number of fundamental analysts consider charting and technical analysis just a step above Voodoo and Astrology. The remainder may look at technical indicators to time entries and exits of securities they have already identified. In those cases, technical analysis is used, but only as a secondary consideration.
People who do technical analysis tend to justify their analysis as understanding the supply and demand for shares, which is how you described it yourself. At some level, I think this is plausible as short term analysis (and the fundamental analysts who use TA for timing decisions would also agree) but long term analysis is harder to justify since both supply and demand can change dramatically over the long term. This can also happen to fundamental business prospects, but these risks are already incorporated through a discount rate reflecting risk, so it’s not as damaging a criticism.
I personally think some technical analysis is plausible, but as an investment shop, it is difficult to have a unique value proposition using technical analysis, whereas it is easier to argue that fundamental analysts have the right training and experience to determine intrinsic or relative value in some specific market niche, and this is one reason why there is more of that. In macro analysis, we do sometimes look at charts for things like support and resistance channels - the basic idea is not that these are magical lines in and of themselves, but that breaking out of these channels is a moment in which long-standing market psychology may change … i.e. a point in which people who are just lazily along for the ride might start to panic and leave, or (in a downtrend) might stop running away and take notice.
Prop shops really are the places where charting is big. To some extent, macro funds also use charting and technical analysis, but macro has been a very hard haul these last few years, and has almost died out (I expect it to revive one day, but for now, it’s suffering)