First off, restaurant silverware is typically not made of silver, but rather of steel or stainless steel. A common steel used in cutlery is 18/10 stainless, which has an austenitic crystal structure. Austenitic steel is normally nonmagnetic, which is why most stainless steel objects are not attracted to magnets.
However, as mentioned on this surprisingly interesting website devoted to steel fastener manufacture:
There are five classes of stainless steel (ferritic, austenitic, martensitic, duplex, and precipitate-hardened) and only one is nonmagnetic (austenitic).
The microstructure of austenitic stainless steel can be changed by a process called martensitic stress induced transformation (MSIT). This is a microstructural change from austenite to martensite and the transformation can occur due to cold working (the process by which many fasteners are made) as well as slow cooling from austenitizing temperatures.
I am not experienced in the methods used in the manufacture of cutlery, but if there is any cold-working used in the shaping of the 18/10 stainless cutlery, martensitic stress-induced transformation might be the culprit behind the ferromagnetism.
Add that to the magnets Enucatl mentions which are sometimes used by restaurants to pick up the cutlery and the hysteresis property of ferromagnetic materials, and you have a possible explanation for why two pieces of stainless cutlery seem to be magnetized and can attract each other.