Your stats "only" increase skillpoint gains, each skill will have a primary and secondary stat assosciated to learning it. The higher those two stats the quicker you gain the skillpoints needed for the skill.
As to what ship skills do, look at the description of each ship.
Merlin
Special Ability: 5% bonus to shield resistances and 10% bonus to Small Hybrid Turret optimal range per skill level.
so where Caldari frigate I gives 5% and 10% as stated, Caldari Frigate V gives 25% and 50%.
example 2: Kestrel
Special Ability: 10% bonus to Kinetic missile damage and 5% bonus to EM, Explosive, and Thermal missile damage per level.
again Caldari Frigate I improves kinetic damage by 10% and others by 5%, Caldari frigate V makes you kinetic missile 50% more powerful and the other 3 25% so.
When you get to ship that require multiple skills
Ill use my Buzzard as this example
Caldari Frigate Skill Bonus: 5% bonus to Missile Kinetic Damage and 5% bonus to Missile Launcher rate of fire per level
Covert Ops Skill Bonus: -98% to -100% reduction in Cloaking Device CPU use per level and 10% reduction to duration/activation time of modules requiring Astrometrics per level
Note: can fit covert cynosural field generators
So at Caldari Frigate V its Kinetic missiles do 25% more damage and all its launchers fire 25% faster. but youll see it also has a listing for covert ops skill.
SO Covert Ops I lets you fit Cloaks in this ship with 2% of CPU normally required by those modules and a 10% boost to Astrometrics modules (i.e. probe launchers)
At Covert Ops V these bonuses become 0 CPU usage from cloaks, and 50% boost to astrometrics modules
Hopefully clarifies it for you a little in my clear as mud stylee.