MAC addresses are PHYSICAL addresses, they are stored in the physical device. They cannot be permanently changed. You can spoof them (change them) but it is not permanent. If you spoof the MAC address of your computers NIC or router or any other device, it will return to its assigned permanent MAC address after you reboot the device. Unlike IP addresses, MAC addresses are Unique, its purpose is to provide a physical address to every node (device). No two devices have the same MAC address, this allows people, routers, servers, etc, to identify a SPECIFIC device on a network.
An IP address is not physical, it is a LOGICAL address. As I said earlier the PHYSICAL MAC address is permanently assigned to a node. However LOGICAL IP address is just as it sounds, it is not physically assigned to computers or other devices meaning IT CAN BE CHANGED. MAC addresses are assigned by the manufacturing company who made to device. IP Addresses are assigned via a protocol known as DHCP (dynamic host configuration protocol). DHCP basically works with DNS server (Domain Name Server). The purpose of a DNS server is name resolution, it matches the name of the destination with its IP address (ex: www.yahoo.com is matched with yahoos IP address.) DHCP via your LAN router assigns you a dynamic IP address which allows other devices/computers on you Local Area Network (LAN) to contact/identify you. However that is not your real address. There aren't enough IPv4 address to go around to ISP and large companies use NAT or Network Address Translation, which is configured and implemented in your router. Your computers IP might be something like 192.168.0.1, but that is not your REAL IP. Your real Ip (static) is probably something like 173.29.x.x. Your static IP is whats used to communicate over the Wide Area Network (WAN) or internet. On your computer lets say 192.168.0.1 you enter www.google.com. Googles web server will NOT recognize you as 192.168.0.1. As mentioned earlier NAT will convert your ip 192.168.0.1 into the REAL IP 173.29.x.x. Your real IP is whats used to communicate on the WAN, your NAT IP (192.168.0.1) is whats used to connect over the LAN. So if you send another computer on your LAN a message they will recognize you by your LOCAL IP (192.168.0.1), however if you send a message to somebody outside of your LAN, your Local IP is converted through NAT into your real IP. The purpose of this, is to save money, bc as I said there aren't enough IPv4 addresses to go around, and this way you can assign a business a router with its REAL IP. The company can now create tons of private IP addresses and it wont cost extra because they are converted on their way out of the network. That router uses NAT to convert messages from private Ip's and relay it to the WAN using the REAL IP. This way companies save money by not having to supply multiple REAL(static) IP's. Company servers will use Static IP's for email and web servers so that they can always be reached. Dynamic IP's are leased from the DNS server and expire wants the lease is up, They change. Many people have the IP 192.168.0.1 but you cannot access their computer over the WAN with that IP only the LAN, from that you can see how a physical MAC is necessary to distinguish between devices.
Now after reading that I can quickly explain MAC addresses importance. You now know about NAT, and how it converts outgoing IP's from the LAN into REAL or static IP to be used over WAN. Now you might be thinking, well how does a router know which computer the IP 192.168.0.15 belongs to and which one is using 192.168.0.18, etc? How does a router receiving a packet know which computer on the LAN to forward it to? This is why you have PHYSICAL MAC addresses, your router has a table that records the computers LOGICAL IP to its PHYSICAL MAC. Computer sending info contain the MAC address in the head and because its physical and unique the router knows exactly who the message was intended for. Now obviously there are ways to manipulate the process (ie ARP spoof, MAC spoof,IP spoof) But the MAC address will always be the same after reboot it returns to its default. A common use for MAC address is MAC filtering. On your router you can enter MAC addresses that you don't want to allow access on your LAN or specify the only MAC addresses to allow. This way the physical device is denied, to ensure greater security.