The Catalyst 2960 switches you are emulating are Layer 2 (L2) switches. Layer 2 switches does not operate on "network" Layer 3 (L3), where IP protocol resides. Instead it works at the "data link" layer (L2), where it only works with MAC addresses in case of Ethernet network. The only IP it might have are only for CPU interface, i.e. for managing the switch via network. Refer to OSI model for more information on network layers.
As you are most likely not using L2 managed switch features (VLANs for example) so this could be simplified to unmanaged network, with unmanaged switches. They don't have IP at all as they aren't configurable. When a packet comes to it's interface it reads source and destination MACs from a packet data link layer, records source MAC/port into it's own forward table, checks that table if the destination MAC are known. If it is, it resends the packet to designated port. If it's not it just sends the packet to every other than the source ports. This works until it learns the correct port when a return packet will come.
I believe Cisco Packet Tracer had a bundled example explaining how this works. I suggest you to learn & understand that part of networking first, before proceeding onto routed networks.
As for your situation as already noted in comments the link between your router and switches are down as indicated by the red dots nearby. Ensure that your router are "running" and links are connected with correct type of connectors. Also make sure you've corrected to a right interfaces of the router with correct networks. You should check which interface of your router has the 192.168.1.101 IP, if it's Fa0/0 for example you should connect that interface to the Switch0. Same goes for right side IP/interface, connect the correct on to Switch1.