Precision

Precision is a base statistic that is directly tied to Critical Chance - a chance to score double (or triple, or quadruple, etc. damage). Normally every ship starts with 3% critical chance, but through precision they can get more. Precision is primarily generated by the equipped Scanner module, and can be further boosted by substats on any module or turret. Critical Chance by itself can also be boosted through substats on turrets.

Precision defines how precise the ship's attacks are, which is relevant for critical hit calculations. The higher the ship level (which is related to the level of the gear equipped on the ship), more Precision is required to maintain the same critical hit chance.

All turrets are subject to the same rule - thus having high precision on a mining ship will cause it to cause critical hits with increased frequency, which in turn speeds up mining considerably.

Precision and Critical chance

At Level 1, a ship with 10 Precision has 3% + 1.86% = 4.86% Critical Chance
At Level 30, a ship with 10 Precision has 3% + 0.25% = 3.25% Critical Chance

There is always a base Critical chance of 3%. Skills that increase the Critical chance will always count towards the base value.

Example: A Skill gives 3% the base Critical chance, and a 2% multiplier.

This calculates to: (3% base + 3% from the skill + ab% from gear + xy% from precision (see below)) * 102% (from the multiplier).

Precision into Critical chance

How Precision translates towards Critical Chance shown in the ship's Info Statistics tab is roughly:

levelScale = round(25 × 2^(shipLevel / 10)) -> shipLevel comes from player level and ship gear

linear = 0.05 × precision / levelScale -> meaning higher the ship level, more is required 
if linear > 5%:
  precisionCrit = 5% + (linear − 5% + 1)^0.75 − 1 -> over 5%, precision gains diminishing returns.
else:
  precisionCrit = linear -> up to 5% is gained linearly
Critical chance = (3% + precisionCrit + flat crit substats) × crit multipliers
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Since this means precision by itself isn't really "human-readable", it's slated for a revamp at a later date.