What game is this?
jdrakeh is correct, it's a game called Draci Doupe, which translates as Dragon's Lair. The game actually has two supported sets of rules. The first set, based on the original rules from right after the collapse of Socialism is version 1.6 and is the most popular. It is essentially the same game as the original, but with tweaks. The second set of rules is called Draci Doupe Plus (Dragon's Lair Plus), but it is actually an entirely new ruleset.
Draci Doupe 1.6 version of the rules is based on an exploding d6 die. For example, when a character attacks, the player rolls a d6 die and adds the number to any bonuses the character and the weapon has to hit. Every weapon has some bonus to hit, that depends on weapon-type. Of course, magic can increase this bonus. When a character hits, the damage caused is equal to the amount by which he exceeded the defense rating of the targed plus the damag bonus (which is also unique to each weapon and affected by things like strength...).
Draci Doupe Plus is a completely new system that is, in my opinion at least, highly innovative and has little to do with the original Draci Doupe. It also relies on d6 dice, but it nonetheless works very differently. Most rolls are 2d6 to achieve some normal distribution approximation, but what is really unique about the system is that it provides a conversion between the bonuses/rolls and in-game measurements. I don't have the rules in front of me right now, so I won't give you the real numbers, but basically, there is a conversion between bonuses and meters, bonuses and hit points, bonuses and weight and so on. When character decides to jump, he will use his jump bonus (modified by appropriate modifiers) conversion and a 2d6 roll to see how far or how high (different modifiers) he can jump, he will use his strength bonus and the conversion to see how much he can lift and so on and so on. There are some general rules to this, such as every +6 bonus doubling the effect and every +20 bonus multiplying the conversion by 10 (there are pre-calculated conversion tables included). It is actually very elegant system, at least in theory. I have not, however, tested the system in practice - my players are not keen on testing new systems - so I don't know how well it actually works in practice. I have played quite a lot of the original Draci Doupe and its revisions in the past, and it worked fine, but I have not done so for many, many years now - having switched pretty much fully to D&D.