system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: how does the geometry of a bike change performance?
gpt
There are a huge amount of factors that go into the geometry of a bike, but the main idea is changing the relationship between the various contact points and components to alter how they work in comparison to each other.

For a few examples;

The angle of the head tube controls the angle that the forks sit at - by changing this angle you change how the forks steer, with a steeper head tube making the forks easier to steer (and more twitchy), a slacker angle harder to steer (and more stable).

The height of the bottom bracket basically sets the height of the rider on the bike - and is a balanv beteeen a higher BB giving more ground clearance for the pedals, while a lower BB drops the centre of gravity and makes it more stable.

The length of the wheelbase (the distance between the wheels) affects how maneuverable a bike can be - the longer the bike the harder it will be to get it round a corner, but the more stable it will ride at speed.

The relationship between the angle of the seat tube, chainstay and top tube length will affect where the riders weight is positioned on the bike and how it will balance - forward is good for ascending, rear descending, and a balance somewhere in the middle.

A lot also affects the riders position - narrower bar is more aerodynamic (loved by the roadies), while a wideone gives more control (loved by the mountain bikers), a long stem stretches out the rider and makes the steering react slower, a short stem moves the rider back/upright and makes the steering twitchier.

Rider comfort is also a big consideration - the best positions for aggressive riding and control, or for aerodynamics are typically not the most comfortable, while a very relaxed, upright position that is comfortable going to the shops is inefficient and gives much poorer control and balance in more challenging terrain.

The biggest thing is that everything alters everything else, so designing the geometry of a bike is a giant balancing act.
If you want to use narrower bars for example then that will make your body more upright, so you would have to change your stem length (which changes the steering characteristics), or get a frame with a longer to tube to compensate. A bike with shorter chainstays will be more maneuverable, but will also have a shorter wheelbase so will be less stable...