Charlotte Lucas spends time talking to Mr. Collins. Elizabeth thinks Charlotte is simply helping out by distracting him, never dreaming that her friend is angling for a marriage proposal of her own.
But Mr. Collins proposes to Charlotte on the Saturday morning before he leaves for Hunsford, and she accepts.
Her acceptance is on purely practical grounds. He's a good man, with a good career, and she's not rich and not pretty.
Plus, she's twenty-seven, which—let's face it—is old.
Charlotte is a wee bit worried about how her friend's going to react, but the whole Lucas family is overjoyed.
Mr. Collins informs the Bennet family that night that he will accept their invitation for a speedy return visit, surprising all of them.
They think he means that he has turned his attentions towards one of the younger Bennet girls and they know that Mary would be willing to accept. (She's plain and bookish and actually sounds kind of perfect for him.)
The next morning, though, Charlotte arrives and spill the beans to Elizabeth.
Elizabeth is all idealistic and (as we'll find out later) twenty years old, but Charlotte is a realistic old maid.
It's a practical decision. She wants a comfortable home and not to be dependent on her parents or brothers to support her. Mr. Collins is really her best option.
Elizabeth finds it hard to believe that Charlotte would throw away every possibility of emotional satisfaction just to be married.
Given what we know about women's options at the beginning of the nineteenth century, we're not as surprised.