Headfairy - av gives you a "fairer" result in your constituency, as the winner will have a bigger share of the voters preference. But it doesn't deliver a fair proportion of the seats for all parties over the country as a whole - you may still get eg 8 labour seats and no green seats even though you use av.
pr systems (there's more than one way of trying to do it) look at the overall number of votes for each party over the country as a whole and try to make sure the number of seats each party gets is proportional to how many people voted for them.
So if there are 100 seats, and 1/100 of the country voted green, you would get one green mp, even if there were no particular constituencies where a green "won".
Its trickier to set up though, and means you may not have a "local mp" for your constituency.
Scotland currently uses a mixed system, so you still have a constituency mp who represents your area, picked by the traditional first past the post syste. But then there are additional "list MPs" who are chosen in a way which balances up the number of constituency mps compared with the overall vote, to make it more fair.