First of all, he asked Miss Lucas. I was so vexed to see him stand up with her! But, however, he did not admire her at all; indeed, nobody can, you know; and he seemed quite struck with Jane as she was going down the dance.
"quite struck with" - Jane has caught his attention and he is showing his interest in her
"going down the dance" - in Jane Austen's day, dancing was not one man and one woman together, but rather were group dances deriving from folk dances. They often had the men and women in lines opposite one another, and each pair would gradually move from one end of the line to the other.
This is a modern picture, but the dance is very like the ones Jane Austen danced: