Number systems are different ways to express numbers. Humans now use the decimal number system primarily probably because we have 10 fingers and initially count using our fingers. In the decimal number system, there are 10 single digit numbers (0,1,2,3,4,5,6,7,8,9).
Computers are electronic/electrical devices. That means things kept in it originally were usually either electricity there or it was not. Now a lot is stored magnetically so easy to say a positive charge there or negative. On CD/DVDs either a hole burned in the media or not. For these reasons, computers work with everything internally in binary. The binary number system is a base 2 number system which means it only has 2 single digit numbers (0 and 1). If you were to look to see exactly what is coming across the network or stored in memory or on your storage device, you would see lots of zeros and ones. However, for normal use the computer changes want it displays from binary to decimal and we see what are normal characters for humans and it does the opposite on what we enter converting decimal to binary automatically.
There are times you want to see exactly what is stored. For instance, you may want to know what the MAC address of a device is. If you displayed in binary (they are shown usually in labels on your network devices) you would see 48 zeros and ones. That would be difficult to read. IP version 6 addresses are similar and longer and would be 128 zeros and ones. Instead we use the hexadecimal number system as it can show in one character what is in 4 binary numbers. The hexadecimal number system is a base 16 number system and has 16 single digit numbers (0,1,2,3,4,5,6,7,8,9, A, B, C, D, E, F), yes letters are numbers. That means the MAC address you see is only 12 hexadecimal characters long and the IP version 6 addresses we see are 32 hexadecimal characters long, which is a lot better and easier to read than the ton of zeros and ones.