What are these codes on game covers?

Solution 1:

In essence, those are unique IDs for each game - at least the PS3 ones. I can't currently find any sources about the X360 ones.

PlayStation 3

Various communities, single users and random sites try to collect these (I couldn't find an actual comprehensive list, though).

One in particular also largely explains the naming scheme:

• ES stands for the European sales region
• US for the NA region
• JM, JS, AS and probably a bunch of others stand for various Asian regions

As per @TML's comment:

• The BC prefix is used for first-party content by Sony and subsidaries.
• The BL prefix, on the other hand, for third-party content.

So, a BCES is a first-party game released to the European market.

It's a unique ID for each released retail version of a game.

And, as pointed out in the comments, it is mostly referred to as a "title ID". "catalogue number" or similar. On consoles, these are usually used to identify game data on the hard disk (savegames and the such).