All of these quantities are telling you something about the relationship between query and match sequences. The least informative among them is score, even though high score generally means more likely to be related. However, score is length-dependent, so a sequence that is 10000 residues may have a score of 1000 with an unrelated sequence, while a sequence that is 300 residue will have a score of 1000 with another and that will actually be a true relationship.
BLAST does something called high-scoring segment pairs, which boils down do making lots of local alignments and scoring each separately. From a combination of those scores a total score is derived. When max and total scores are the same, that means that there is one global alignment between the two sequences, which is usually good because it means that they can be aligned well without long insertions or deletions.
An E-value is not length-dependent and is usually more indicative of a true relationship than a raw score. As already explained, it represents a likelihood that the observed alignment could have been made by chance. In your case the E-value is zero for all practical purposes.
Percent identity tells you how related the two sequences are in terms of evolutionary distance. Yours are fairly divergent, which likely means that they have been separated by long evolutionary history.
A coverage of 97% tells you that the two sequences have the same overall organization and length. Along with identical total and max scores, that indicates that the two proteins are likely to perform a very similar function, and possibly an identical function. If the coverage was 30%, it could mean that the two sequences share only a single protein domain between each other, in which case they would be more likely to perform somewhat different functions.
All combined together: 1) percent identity tells us that your two sequences are very distant in terms of evolution (say, one was from yeast and another from human); 2) E-value tells us they are clearly related to each other; 3) scores and coverage tell us that they likely perform the same function.
NCBI has several resources available on this page that should be useful. Statistics of sequence similarity scores is covered here.
Genomax's linked resources are all you should need to know, but the TL;DR is that these statistics tell you different things about how accurate/meaningful your alignment is. Coverage for example, tells you whether you have a short or long alignment, and combined with identity can tell you whether you have a long, low identity match (e.g. perhaps an orthologous genes), or a short, high identity match (similar protein domains/active sites). The E-value is a description of how likely it is that the match could have arisen effectively by chance, so you want this number to be as low as possible. A lot of people/tools use a default of 1E-6, but this is pretty arbitrary.
Thank you so much to both of you.. Joe could you apply what you said to my example? In my specific case how are these two parameters related? Again, sorry if it's a banal question, but this is all new and math is not my strong point and material example help me in understanding. Thank you so much for your time!!!