With the Java Virtual Machine, data (objects, arrays of primitives) is stored in the heap which is a shared region of memory that all JVM thread can access. Memory is allocated for the heap when the JVM starts (and may expand to a certain limit at runtime depending on the configuration). Whenever a new object is created, a portion of the heap is allocated to store it.
When the heap is full i.e. when no further allocations can be done (this is an over simplified version, I'm skipping details), the garbage collector is started automatically to reclaim memory space. Basically, any object which is not referenced by an active thread may be safely de-allocated.
Note that the garbage collector thread normally runs as a very low process thread but, once kicked in, it can not be suspended until the task completes.