Logic behind ECO openings

How are the openings classified? As in, what does the 'A' stand for in A27 or the '16' in C16?

A00 [Start position] 
A10 [English]  1.c4
A20 [English: King's (1...e5)]  1.c4 e5
A30 [English: Symmetrical]  1.c4 c5
A40 [Queen's Pawn Game]  1.d4
A50 [Indian: 2.c4]  1.d4 Nf6 2.c4
A60 [Benoni: 3.d5 e6]  1.d4 Nf6 2.c4 c5 3.d5 e6
A70 [Benoni: Classical]  1.d4 Nf6 2.c4 c5 3.d5 e6 4.Nc3 exd5 5.cxd5 d6 6.e4 g6 7.Nf3
A80 [Dutch]  1.d4 f5
A90 [Dutch: 2.c4 Nf6 3.g3 e6]  1.d4 f5 2.c4 Nf6 3.g3 e6

Seems pretty random, B's and C's are kingpawn games

The only thing I know is the variations of one opening usually have the same letter... Otherwise I barely see logic in it.

Even I don't see the logic in it...

Btw.. A00 is the Ware opening AND the Amar opening, not the starting position, and both are completely different openings.

ECO openings is a system which is used to go systematical through the openings.

For that, we used A-E, to classify the starting moves. The 1-99 after the letter is where it is in the system. A big opening, lets say ruy lopez (1: e4 e5 2: Nf3 Nc6 3: Bb5) got alot of numbers, because it is a big opening. A lesser opening got less numbers because that there is not so many sidelines.

A is:

Openings not starting with 1: e4 or 1: d4 (english, birds and so on) (A00-39)

1: d4 without by 1: .. d5 or 1: .. Nf6. (A40-44)

1: d4 Nf6 without 2: c4 (A45-49)

1: d4 Nf6 2: c4 without g6 or e6. (A50-79)

1: d4 f5 (A80-99)

B is:

1: e4 without 1: e6, e5 or c5 (B0-19)

1: e4 c5 (B20-99) (A classic example of extremely big opening)

C is:

1: e4 e6 (C0-19)

1: e4 e5 (C20-99)

D is:

1: d4 d5 (D0-69)

1: d4 Nf6 2: c4 g6 with d5 grünfeld (D70-99)

E is:

1: d4 Nf6 2: c4 e6 (E0-59)

1: d4 Nf6 2: c4 g6 (without d5) (E60-99)

That's rather complicated, and not easy to understand at all...

Why are there so many variations anyways? And how do they arise?

You can find a full explanation here
https://en.wikipedia.org/wiki/List_of_chess_openings 
"Why are there so many variations anyways?" Because so many games of chess are played
"And how do they arise?" They arise after grandmasters play them. Opening theory is the practice of the grandmasters.

thanks