There are several points to better bike components (frame, wheels included):

• Durability
  • Chinesium (not made in China but crappy Chinese parts) parts are usually less durable. Softer steel on axles, bearings. Softer aluminum on frames and wheels that bend permanently with a bit of abuse.
  • Low end Shimano parts, low end reputable aluminum frames and wheels are made from appropriate materials and are significantly more resistant to wear and abuse. They're often close to bulletproof. Higher end parts up to SLX/105 could be more durable still. Above that weight savings might eat into durability.
  • Another component that I'll ascribe to durability is the ability to retain adjustment. That is to keep operating as adjusted without the need to readjust afterwards.
• Niceness to use
  • This refers specifically to drivetrain. Nicer components are nicer to use. The physical feel of the action of control levers feels nice.
• Performance
  • Better components shift faster, cleaner, can shift under load. For example there's dramatic difference in the shifting performance between say Shimano Tourney (bottom of the barrel) and SLX. Both work fine though.
  • Better wheels and tires are typically lighter and allow for significantly faster acceleration.
  • Reputable brakes can have significantly better performance than Chinesium ones. This directly translates in shorter stopping distance in emergency.

If your bike has a decent aluminum frame and a workable drivetrain, the cheapest thing that would make the most obvious difference is replacing the tires with something light and narrow. Keywords Schwalbe, Panaracer, Continental, etc. Next up would be replacing the wheels too. Mavic Aksium used to be a bombproof and light entry level wheelset. There might be better value alternatives these days. Once you're happy with the wheels, I'd spend money on comfort - correct saddle for my ass, stems, handlebars so that my riding position is as comfortable as possible. Only then I'd spend money on upgrading the drivetrain.

If the frame is garbage, then I'd start with a new (could be second hand) bike that has a decent aluminum frame and low end Shimano (Ideally Alivio/Acera) and if possible with Shimano/Tektro hydraulic brakes. Those usually come with decent wheels too and sometimes even with decent tires.