Can somebody explain to me what the terms "dependent" and "independent" means when describing verbs?? Sorry, I'm sure this is a very basic question....

Does English has dependent and independent forms of verbs?? How does a language evolve to have these features??

Dependent are Irish verb forms following most verbal particles and conjunctions. (They "depend" on those.)
Independent (absolute) verb forms are without verbal particles (except direct relative a, past particle do, má, mar etc.)

Today, the differences are mostly confined to irregular verbs. (e.g. bhí vs. raibh)

A short explanation: The reason was strong stress on first syllables of verbs which led to merging and loss of endings in dependent forms but stressing on preverbs when they came "first" (next to particles).
(eg. [do-]bheir vs. tabhair, deir vs. abair, etc.).

No, English verbs doesn’t have dependent verb forms.