In the early days when you had to be really computer expert to really own or use a computer, what were the things computer was capable of doing?

Prior to the Internet there were many dial-up bulletin board systems (BBS).  Hopefully you had one locally so it didn't cost a fortune to call one.  There were times when I called long-distance BBSs, which coincided with the times I had my computer privileges taken away. BBSes had sections like message boards, file repos, multi-player games, etc. They were like a much better organized IRC. Often BBS owners would call other big BBSes and post ads for their BBS, so you would build up a directory of numbers. One of the most magic moments for me with a computer was the first time I heard sampled audio reproduced.  Many early computers had a 'datasette' - a data version of audio cassettes used as an inexpensive alternative to floppy drives. Early computer speakers could usually only make a 'beep' sine wave sound, or if they were more advanced you could control the duration and pitch of the sine-wave beep. Someone wrote a program to use the zero-cross functionality of the datasette to sample analog audio stored on an audio cassette. They would then make the speaker 'pop' or 'click' instead of 'beep' at the point the audio waveform crossed the origin.  The result was sampling and playback of music as 1-bit audio. The first track I ever heard was about 5 seconds from a Prince song on an Apple ][. That's all that could fit in memory. Unfortunately Google has failed me to provide an example to share.

In the earliest days, computers were necessary to do massive number crunching that humans could not, like tally the US census, predict expenses and earnings for multinational companies, make firing tables for new cannons (what direction, height and charge, to get at what coordinates, at all possible wind speeds, wind directions, pressures, and so on), direct trains to avoid collisions, et cetera. Limited industrial automation also became a reality. Later when companies and people started getting desktop computers, the major "excuses" to get a computer was spreadsheets, accounting, typing/printing letters and other publications, databases, educational/instructional software (lots of mouse training tutorials back then)... And when modems and network cards came on the scene, it became more and more about communicating, BBS, sending orders remotely, central inventory management, working remotely on mainframes, and so on. Then Internet came and gave us home shopping, multimedia, %*=+@#!~ Real Player, animated cat pictures... the rest I think you know.

I assume by "earliest" computers you do not really mean the turing machine. Getting a PDP mini clone do the work of entire payroll department seemed pretty cool to me back in 80s. Other than that.. my first "in-depth" exposure to PC architecture came in early 90s while trying to install Wing Commander for DOS. I think the game required all 640K of "primary" RAM. Then there was a genuine amazement mixed with wow and curses when game crashed