Multiple switches - how does it work?
Solution 1:
If Switch 1 doesn't know what port the frame (not packet!) is meant to go to, it will flood all ports (except the port the frame originated from). One of those ports will be connected to Switch 2, which means Switch 2 gets the frame.
If Switch 2 doesn't know what port the frame is meant to go to, it will flood all ports (except the port the frame originated from). One of those ports will be connected to Computer B.
So Computer B eventually gets the frame, meanwhile all other devices ignore it.
Now you can connect the dots. When Computer B responds, Switch 2 will learn that frames destined for Computer A go to the port that has Switch 1 connected to it, and Switch 1 will learn that frames destined for Computer B go to the port that has Switch 2 connected to it.
Solution 2:
Physical port on a switch counts as OSI layer 1. All MAC addresses that arrive into this particular port represent physical addresses of network devices (OSI layer 2). On each active port, there can be 0, 1 or more MAC (or CAM or whatever switch vendor names them) addresses. In fact, switch does not have a clue what type of device is connected without additional information (either administrator or some specially designed protocol tells more).
So, connecting a switch to another switch, all MAC addresses that one switch knows can be replicated to another switch. If it is a dummy switch, then all MAC addresses contribute to the same unnamed LAN. If it is a better one, it can have configured multiple virtual LANs (VLAN) and every VLAN has its own set of MAC addresses. They can be repeated in more than one VLAN.
If a switch receives the same physical address through more than one interface, it is usually detected and counted as "MAC flapping". It means that switch can not be sure through which port a packet with certain MAC address is to be sent.
Switches usually forget about MAC address on a port if it does not appear in last few minutes. This is good; otherwise switches can receive too much information which can be contradictory over the time.
Occasionally, due to network error or a hacker attack within a network, some device(s) can generate a lot of MAC announcements. If the number of announced MAC addresses is too high for switch to remember, it can decide to forget about optimal packet delivery. If not sure, on what port a MAC address resides, a packet can be transmitted to all ports like a broadcast (an attack with name arp-spoofing succeeded).
If administrator is aware of potential risks, it can pose a limit on how many different MAC addresses can possibly appear on each port. If it is known that through a port only one computer at a time is connected, then it can be configured as "we can have only one mac" (the type of port on your sketch from Computer A to Switch 1). If it is not known, or another switch is connected to a port, limit can be reasonably raised or even left as unlimited (on an average switch, unlimited is in fact few thousand).
Hope it helps.