Every fella on both teams has to have a go at batting, no choice. Once every player of one side has had his turn batting it's the other sides turn......in this case NZ had beaten the English score with 8 players still to take a turn. ie, beaten by 8 wickets, which is a lot.
A 'wicket' is the arrangement of wooden things the bowler (pitcher) aims at, you hit the wicket with the ball and the player 'at bat' is out. Slang usage has made 'taking a wicket' mean 'got a player out' over the years.
An 'over' is a set of....pitches. Every 6 pitches the bowler has to change to another player, a set of 6 pitches is called an 'over'. Except a pitch is called a 'delivery' and has to bounce once before reaching the crease. The 'crease' is like.....the batters area, like the goalies area in soccer, special rules about ball handling are in force when the batsman is behind the crease. From here on it gets a bit mystical, some teams use the bats blood and frog spawn rule.