When we see something, how and where in the brain do we remember it and are able to recognize it later?
What happens in the brain that makes this possible?
The current working theory (note this is still an open question, but there are many leads being followed):
Sensory systems receive a combination of signals from an event, which are initially bound to the hippocampus (this is called episodic memory). Then, typically during sleep, the memories are consolidated.
A simplified view is that consolidation basically consists of communication between the neocortex and the hippocampus, and the memories are thought to be "saved" in the neocortex. Thus, amnesia patients with hippocampal damage still have all their long-term memories, they just can't create new memories (because their old memories were already consolidated to neocortex).
Your neocortex has many subregions with many functions. One is the temporal lobe, where semantic memory seems to be stored. So your episodic memory may record several interactions apples and, over time, your semantic memory will be updated (as memory consolidation occurs) to "consolidate" your concept of "apple".
The temporal lobe is highly connected with the occipital lobe (where visual information is processed) and the two likely work together to identify objects using the consolidated information.
On the molecular level, how the memories are actually stored. The most well known concept is connectionism: different connection strengths between neurons carry different information. But there's also genetic expression going on, and there was recently some research on prion-like proteins contributing to memory as well as astrocytes.
Realize, of course, that a lot of this is cutting edge research... and therefore could be wrong or contain numerous oversights and simplifications.