Clinton and Obama have mobilized different parts of their party. She appeals to the blue-collar voters, and Obama has been more successful with affluent, well-educated Democrats

1. What does it mean 'to mobilize different parts of their party"?

2. Can 'the' be removed?

Thanks in advance!
1. They have inspired them to be active in the political process.

2. Yes. It was used to emphasize the blue-collar workers in the Democratic party; the Republicans have blue-collar workers too. Note that in the Obama portion of the sentence, it specifies Democrats.
Thanks, GG!