What advice does Catherine give to Raina? Why?

Catherine is status-conscious and eager to keep up with the latest fashions of genteel society. She wants her daughter to marry someone with high social prestige and wealth, and her advice -- explicit and implicit -- is that Raina shouldn't let a "good catch" get away. Raina should waste no time accepting Sergius; she should play the straightforward role of a dutiful, devoted fiancé.
At the end of the play, when it appears to Catherine that Bluntschli is a very high-status, wealthy man, she tries to pressure her daughter to accept him as a husband.
It's perhaps surprising how little Catherine attempts to advise her daughter, given what we learn about her commanding, opinionated personality. As we're told in the stage directions, she is "imperiously energetic." She is a controlling influence on her husband, manipulating him easily. She has more sway over Nicola than her husband does, and in Act III her husband recognizes that she is better able to issue compelling commands to his men:

They'll be far more frightened of you than of me.

But Raina is a forceful character in her own right, and so we get the impression that maternal lectures would do little good. The most explicit advice Catherine ever gives Raina happens in the first act, when she urges Raina to embrace her position as Sergius's betrothed. She tells Raina of Sergius's victory, noting he's "hero of the hour," and implies that Raina has shown a foolish hesitancy about the match -- he's the most eligible bachelor possible:

And you! you kept Sergius waiting a year before you would be betrothed to him. Oh, if you have a drop of Bulgarian blood in your veins, you will worship him when he comes back.

We suspect that Raina is worried Sergius will get away. He's an especially hot prospect now. Later, in Act II, Catherine questions Raina about what really happened that night with the Swiss soldier. She urges her daughter to be discreet, so as not to endanger the engagement:

Oh, Raina! Raina! Will anything ever make you straightforward? If Sergius finds out, it will be all over between you.

Finally, in the last act, Catherine tries to pressure her daughter into accepting Bluntschi. She doesn't offer any explicit advice to her daughter about this; rather, she presumes to speak for Raina in front of everyone:

Then, Captain Bluntschli, since you are my daughter's choice, I shall not stand in the way of her happiness. [Petkoff is about to speak] That is Major Petkoff's feeling also.