Hi there everybody. One of my quests is to fill a black soul gem and take it to some guy his name escapes me. Sorry to sound silly but I don't even know how to fill a soul gem, what is the significance of doing so and does a filed soul gem have any powers etc? Thanks.

you have to use the spell "Soul Trap", or a weapon enchanted with it..

soul gems are used to refill magic weapons charges, or in enchanting

There are two types of soul, Black for mortals, and white for animals and monsters (including intelligent races). White souls have different strengths, a wolf has a weaker soul than a wispmother, and there are different strengths of normal (white) soul gems, but all black souls and all black gems are grand, same as the most powerful white souls. To fill a black gem, use soul trap on a mortal (any of the races you can play as) before you kill them.

This is considered for the most part evil, though the Elder Scrolls world is more ambivalent on this point than many other fantasy worlds. If you don't want to be 'evil' try using it on a necromancer, as it was necromancers of the Worm Cult who invented black soul gems in the first place, karma and all that.

Also do not forget that a larger soul gem (Greater, Grand, Black) can trap souls of lesser beasts. Just because a soul goes into a Black soul gem does not mean it automatically filled with a Grand soul

There is a bug, don't know if it was fixed (I buy filled gems, never used soul trap in Skyrim, Oblivion was a very different story) where if you waste a large gem on a smaller soul, it empties if you drop it so you can be more careful next time.

This is true. I use that "bug" often

What I did was put a soul trap enchantment on a dagger. If I need to fill a gem I'll use my sword to nearly defeat the enemy. Then with them only having a sliver of health I'll pull out the dagger and finish them off with it thusly capturing their soul.