On the surface level, The Wasps shows the general theme of modern beliefs against traditional, or old age against youth. At the same time, the play makes many contemporary references and has themes connected to politics of the time. Most notably, Aristophenes gives his protagonist, Philocleon (literally 'love of Cleon'), a name similar to that of a controversial public figure named Cleon who, although a victorious military leader of the time, was accused by some of exploiting the legal system.
The conflict in the comedy centers on an old man and his son. At the beginning of the play, Philocleon, an elderly juror, has become so addicted to being in court that it has severely affected his health. His son Bdelycleon (or Anticleon) places his father under house arrest. As his father attempts variously to free himself, his behaviour might remind the audience of his infamous namesake: he extols his love of being a juror, both for the influence it gives him as well as the pay; and, at the end of the play, he becomes excessively drunk, assaults other people in public, and causes general chaos when he attempts to talk his way out legal action against him. Although the play does end with Philocleon redeeming himself - his final enthusiastic dance with the chorus wins their approval - his actions throughout highlight the serious theme of the decline of Athenian morals, here linked to the misuse of the legal system.
However, the basic theme of modern and traditional values connects to the plot in a complex way. At the beginning of the play, Philocleon's young son Bdelycleon (or Anticleon) tries to break his father of his habit. In his efforts, the son imprisons him at home, debates with him about the merits and ills of the jury system, but finally agrees to show his father a good time (after defeating him in a farce-trial about dogs and cheese). His father, however, becomes excessively drunk and causes a public row. In the end, he is dragged home by his son, though he emerges moments later to dance with the chorus in the final exodus. This conflict alone introduces the themes of injustice towards the old, the injustice of the modern courts, and the general decline that accompanies old age.
This should get you started thinking about the themes; you will of course need to consult other sources. (Some are listed below.) Fortunately The Wasps is a very fun and well written play, not far from a Monty Python sketch.
Note especially the words of the chorus when looking for evidence of themes. Here are a few quotes (out of context) to get you started with various ways the chorus highlights the theme of old age:
Is not old age filled with cruel ills? What violence these two slaves offer to their old master! They have forgotten all bygones, the fur-coats and the jackets and the caps he bought for them; in winter he watched that their feet should not get frozen. And only see them now; there is no gentleness in their look nor any recollection of the slippers of other days.
Later in the play, they also say:
Should any among you spectators look upon me with wonder, because of this wasp waist, or not know the meaning of this sting, I will soon dispel his ignorance. We, who wear this appendage, are the true Attic men, who alone are noble and native to the soil, the bravest of all people . . . there is nothing in the world more to be feared than the Attic wasp . . . 'tis to us that Athens owes the tributes that our young men thieve to-day.