Broadway's 'Cats' is a show to make audiences purr; Cats.Musical extravaganza with music by Andrew Lloyd Webber, based on ''Old Possum's Book of Practical Cats,'' by T.S. Eliot.Directed by Trevor Nunn. Choreographed by Gillian Lynne.

For many weeks two sulfurous eyes have stared out onto Broadway from the black expanse of billboard above the Winter Garden Theater marquee. Although they intimated mystery, those great yellow orbs didn't fool any moderately knowledgeable passerby. The eyes belonged to one of Old Possum's Practical Cats, from the verse book by T. S. Eliot. But now - thanks perhaps to Gus, the theater cat - the cats are finally and officially out of the bag.

In other words, the long-awaited and much-heralded ''Cats'' has opened. The American interpretation of the London musical hit was worth waiting for. It's enough to make a critic purr. With director Trevor Nunn to marshal the feline aggregation and with choreographer Gillian Lynne to keep these nimble cats on their pretty paws, the Andrew Lloyd Webber musical is a marvel of showmanship and a spectacle to remember.

The interior of the Winter Garden has been transformed into an environment suggesting an enclave within a giant rubbish heap. The debris of consumerism surrounds the stage and reaches up to the boxes and balcony. The bits and pieces so carefully strewn by designer John Napier are, of course, magnified to create a cat's-eye view of civilization. When the house lights go down, a thousand tiny eyes suddenly gleam in the dark shadows beneath lighting designer David Hersey's pale moon.

Gradually from the wings, down the aisles, from upper reaches, the silent cats begin to appear, in some cases even making civil cat overtures to favored spectators. Immediately, the ''midnight dance'' gets under way with ''Jellicle Songs for Jellicle Cats.'' Thereafter, Mr. Lloyd Webber has a ''Jellicle Ball'' with Old Possum and his numerous, highly individualized cats. By evening's end, in the words of gently sagacious Old Deuteronomy (Ken Page), ''You've leared enough to take the view/That cats are very much like you.'' Anyone who leaves the Winter Garden not knowing how to ''Ad-dress'' a cat, simply hasn't been paying attention.

Without presuming to challenge Old Deuteronomy, however much we may resemble them, there are few among us who can sing and dance and cavort like the marvelous cast of ''Cats.'' One and all shine in their several and separate ways. To recall a few: there are the breathtakingly agile Mr. Mistoffolees (Timothy Scott); Bustopher Jones and Gus, the Theater Cat, who is metamorphosed into Growltiger, (all played by Stephen Hanan); Munkustrap (Harry Groener); Grizabella, the bedraggled Glamour Cat (Betty Buckley), with her haunting ''memories''; and the tap-happy Old Gumbie Cat (Anna McNeely). There are also Skimbleshanks (Reed Jones), the ever obliging Railway Cat; Macavity (Kenneth Ard); and the Rum Tum Tugger (Terrence V. Mann), who ''will do as he do do/And there's no doing anything about it.'' And there are others too numerous to mention. Mr. Lloyd Webber has written songs to match all their airs and graces, their moods and cat attitudes.

Before ''Cats'' opened, Mr. Nunn told an interviewer that he had originally envisioned it as an intimate musical, but that Mr. Lloyd Webber had wanted something more. Eye-filling as they are, the special effects at the Winter Garden occasionally do tend to become almost too much. But the joy and relish with which the score is performed under the baton of Stanley Lebowsky plus the brilliance with which the singer-dancer4 ecute Miss Lynne's dazzling choreography reassert the intrinsic virtues of the occasion. Whatever its mood, this is a moving show.