Wow. That's a really broad question, but I'll try to answer it, first in the lawyerly way, and then in the normal-person way.
A "nuisance" is, by definition, "Anything which is injurious to health, including, but not limited to, the illegal sale of controlled substances, or is indecent or offensive to the senses, or an obstruction to the free use of property, so as to interfere with the comfortable enjoyment of life or property ...." Civil Code section 3479. A landlord can evict you for "maintaining, committing, or permitting" a nuisance on the premises that you rent. See Code of Civil Procedure section 1161.4. If you are in a rent-controlled unit in Los Angeles, creating a nuisance is one of the twelve permissible reasons for eviction under the Municipal Code. See L.A.M.C. section 151.09 A. 3.
So what does that really mean? It means if you're tearing up the place or bothering your neighbors so much that it interferes with their ability to live in their apartment, the landlord can, and in fact has a duty to, evict you. Examples of annoying nuisances are (1) if a tenant is cooking meth in the apartment and the fumes are going into other apartments, or (2) a tenant is selling drugs and has traffic coming an going at all hours, or (3) a tenant runs up and down the hall naked screaming obscenities at the top of his lungs. These are all things that would annoy the nuisance-maker's neighbors enough that it affects the value of their apartments.
It is important to remember that by definition a "nuisance" is something that interferes with someone's enjoyment of their own property (including a tenant's leasehold interest in property). Sometimes, a landlord will try to evict a tenant for creating a nuisance, but the only person who comes to testify is the landlord, and he does not live at the property. If that happens, there is no nuisance because the landlord cannot testify that other people in the building are annoyed (that's hearsay). The landlord has to bring as a witness at least one tenant that will testify that the nuisance-maker is interfering with his ability to enjoy his apartment.