The letters A, T, C and G represent the nucleotides or nitrogenous bases that make up a strand of DNA:
A = adenine
T = thymine
C = cytosine
G = guanine
Adenine and guanine are a class of molecules called purines and cytosine and thymine are in a class called pyrimidines. Adenine pairs with thymine and cytosine pairs with guanine. The two opposite DNA strands in the double helix are made of of these base pairs. Purines are larger than pyrimidines so consistent spacing is maintained by each base pair having a purine and a pyrimidine. The sequence along one strand is the "complement" of the sequence along the other strand, so that when two strands are bonded each base is paired with its complementary partner.
The strand shown in the question,
A-T-T-C-G-G-A-C-T-A, is paired with this complementary strand:
This allows A and T to pair and C and G to pair. Each base hydrogen-bonds to its complementary base. The hydrogen bonds are broken when the DNA "unzips" during replication.