The entrances and exits that Oscar Wilde adds to the performance guidelines of The Importance of Being Earnest add tremendous dramatic value to the dynamics of the characters.

Wilde, as a well-balanced author, often rests the plot on basic dyads, that is, on groups of two. We have the themes of double life and secrecy shared by Algernon and Jack.  Similarly, the themes of fantasy and oblivion are well-represented in Cecily and Gwendolen. Repression and confusion are shared by Dr. Chausible and Miss Prism. Therefore there is a lot of drama that  in the dialogues and personal exchanges of every dyad in the play.

For this reason, Wilde is very careful on how to end each conversation, using exits to basically point out that the discussion of a particular theme is over. However, his exits are often dramatic, which brings force to the dialogue. In this particular play, this happens in two particular ocasions.

In Act I, during the conversation of Jack and Lady Bracknell (who remains as the "lone" character of the story), we see a very dramatic exit by Lady Bracknell after she completely insults Jack for not having a name and heritage to offer.

Lady Bracknell: You can hardly imagine that I and Lord Bracknell would dream of allowing our only daughter—a girl brought up with the utmost care—to marry into a cloakroom, and form an alliance with a parcel? Good morning, Mr. Worthing! [LADY BRACKNELL sweeps out in majestic indignation]

In Act II we see a similarly dramatic exit by Gwendolen and Cecily when they find out that none of their fiances, neither Jack or Algernon, is actually named "Ernest".

CECILY:

When the ladies leave the scene, they do it with the full intention of being chased by the men. This does not happen. The two men get completely distracted by the cake and muffins at the tea table and sit down to argue..and eat.

As far as the entrances go, we know that they are not as dramatic but they are surprising, they also serve for the purpose of courtship. For example, Dr. Chausible shows up in Jack's house to be able to see Miss Prism. Algernon merely invites himself to Jack's country estate and enters through the garden as he tries to "sneak in" to meet Cecily. Gwendolen's visit to the country house is followed by Lady Bracknell, who follows Gwendolen, as she knows that she is trying to see Jack. That is how they all find themselves in the same location at the end of the play.

However, Wilde also adds spice to the exits and entrances through the characters of Lane and Merriman, another dyad, who are the servants of Algernon and Jack, respectively. As menservants, they are witnesses to all the craziness that goes on. Hence, their entrances, particularly those of Merriman, are often "announced" by a loud cough as to warn them of him being there.

Hence, The Importance of Being Earnest makes use of exits and entrances to mold the beginning and the end of dialogues and situation, not without adding to it drama, imperiousness and comedy.