Women during that time relied on men to sustain their family, so daughters were commonly married off quickly to a man that looked as if he could provide for his wife and (eventual) family. Mrs. Bennett is eager to marry off her daughter because Mr. Bennet has died and she needs to marry one of her daughters off to ensure she is taken care of by her daughter’s husband. I hope I explained this right!
During a soliloquy, the character is just vocally presenting his thoughts without regard to the audience. The characters are basically talking to themselves. In an aside, the character wants to talk to the audience and is aware of it.