Loyalty affects the number of Credits you earn when mining and the amount of damage that you do. The time needed to gain a certain Loyalty can be calculated with the following formula:

y=45x(x-1)-20

X = the amount of Loyalty

Y = the time needed to reach "x" Loyalty (in seconds)

Loyalty display

With the Galaxy VIP Gamepass, you start with 3% Loyalty. Loyalty Boost also takes effect.

During Endgame, Loyalty is gained 150% faster, meaning each level takes 2/3^rds as long to reach. Being in combat may also affect loyalty gain, but such information is unverified.

Loyalty saves even when you leave, as long as you join the same faction as before.

Either the formula above is incorrect or the loyalty gain in a vip server is different, as testing was done and the times are incorrect.

Loyalty and Starbase Requirements

Required Loyalty	Time Taken to Reach Required Loyalty
11%	1 hour, 22 minutes, and 10 seconds
9%	53 minutes, and 40 seconds
7%	31 minutes and 10 seconds
5%	14 minutes and 40 seconds
3%	4 minutes and 10 seconds
2%	1 minutes and 10 seconds
0%	0 minutes 0 seconds

Trivia

It would take approximately 5 days, 3 hours, 44 minutes, 40 seconds to reach a Loyalty of 100% (without endgame) before the cap was added.
As of version .64e, Loyalty was capped at 30%. New records can't be set anymore. This cap was raised to 33% in version .71c.
It would take approximately 13 hours, 11 minutes, 40 seconds to reach a maximum Loyalty of 33% without endgame.
As of version .61h, Loyalty increases 25% faster than before.
As of version .68a, Loyalty and Starbase level requirements to spawn certain ships have been lowered.
The "Loyalty Saving Update" was done in response to the then-famous "GUI glitch," which made it impossible to interact with any Starbase or ship GUI screens, rendering the game nearly unplayable for those that it befell. The only known way to fix it was to rejoin the game, which previously meant all Loyalty was lost. This glitch has now been patched.
Loyalty is no longer a ship spawning requirement .76c1