As per the Path of Exile Official Wiki, the formula for actual hit chance is:
Attacker's Accuracy / ( Attacker's Accuracy + ((Defender's Evasion / 4) ^ 0.8) )
This means that accuracy is used to counteract an opponent's evasion, and vice-versa, with more evasion points needed the higher evasion gets, and also with more accuracy rating needed the higher your chance to hit. There are, however, a number of caveats:
The actual chance to hit is normally capped to between 5% and 95%.
Resolute Technique allows an attacker to have 100% chance to hit, no matter what, at a cost of never scoring critical hits.
Unwavering Stance allows a defender to become immune to stuns, at a cost of all attackers having 100% chance to hit against them.
There is also a Chance to Dodge statistic, which is a second check, independent of evasion/accuracy.
The actual hitting/missing is not technically a random chance, but uses a mechanic called 'entropy' to even out short-term streaks of hits/misses.
A good resource is the first post in this thread on the Path of Exile forums about accuracy/evasion, which includes a link to a Google Doc with several charts of evasion vs. accuracy and average monster stats at various levels.