Base 64 is how they encode attachments in EMAIL.

You may have heard of HEXIDECIMAL which is 0123456789ABCEF.

When you do math it is usually base 10.   This means you use digits from 0 to 9 for all of your math.

So if we use two digits we can store the number from 00 to 99.

Hexidecimal has 16 symbols.   So we can store values from 0-15 in one digit.

In two digits it can represent a value from 00-FF  which in Base 10 is (0-255).

So just by adding more digit types we can store more information in the same amount of space.

Base 64 uses something like:
0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz/+

So each digit can store a value from 0-63.   So in the example above that would be:
00 to ++ which in base 10 is (0 to 4095) using only TWO digits.

There is a computer technical reason why both Base 64 and Base 16 are desireable in terms of how they fit into memory.

Mainly what you need to know is that you can take any binary file or data and convert it easily to and from base 64.

You end up with a lot of plain text gibberish, but this could be in a post with something like.

[CONTRACT]
Base 64 gibberish
[/CONTRACT]

Steemit or any website could be designed to filter out that contract block, or display it however you want.

We could potentially infinitely extend steem this way with the existing services.   The only drawback is the unsightly appearance of the BASE 64 block data.   If the website hides that or turns it into something useful it would not be a problem.

Base 64 encoding is just a way to encode binary data as a string of text using 64 different characters.

64 is 2^6, and all powers of 2 pop up in computing all the time, because binary is base 2 (as is the I Ching).