You have not shown the code that produced the plot, so this answer is my best guess.
The lines in the plot show the derived survival probabilities and the colored bans show the calculated X% confidence intervals on those values where X is probably 95. If the experiment was run many times, we would expect that the "true" survival probabilities would be within the confidence interval X% of the time. Since the confidence intervals of the curves have a lot of overlap, we cannot tell whether the "true" value of one curve is higher or lower than the value of the other curve.
The value labeled p is meant to answer the following question. "Assume that the two populations have the same survival probability. If the experiment were run many times, what fraction of the time would the observed difference be at least as extreme as the difference that was observed in the actual experiment?" The answer is that the difference would be as large or larger than the one you observed 71% of the time. In other words, the observed difference is not inconsistent with the assumption that the survival probabilities are equal. The survival probabilities could be equal and produce similar data frequently.
Keep in mind that I constructed those answers without knowing how the plot was made. Think carefully about whether they make sense.