Why is Socrates so influential?
There are two kinds of responses people make to this question, because Socrates affected later philosophy in at least two ways. First of all, he must have been an extraordinary person, both charismatic and counter-cultural. He seemed to embody the values he inquired into. As a result he could ask probing questions about what a friend is without failing to be a friend. He could ask whether anyone understood courage, but ask as a courageous person rather than as a coward looking to undermine the virtue.
He struck his friends as possessing what we call a sixth sense, what he called a "sign" that a spirit brought him in certain circumstances.
That is Socrates the person. Meanwhile Socrates philosophized in a systematic way, trying to develop a new way for human beings to analyze and assess difficult concepts, and especially the concepts of moral and political philosophy. He was not the first ancient intellectual to prioritize thinking about values ahead of thinking about the non-human universe (the Sophists, to name only one group, preceded him there). But he seems to have been the first to work out methods and goals for identifying disputed terms and clarifying them through general definitions.
After his death the many friends and associates of Socrates expressed his influence on them in different ways. Some started philosophical circles, even what we today call a school -- Plato in the Academy, for instance. Others, like the early Cynics, emulated Socrates the person with (as far as we can tell) little interest in any particular doctrines or the arguments to defend them. For them Socrates was overwhelmingly the subject of anecdotes, a man in plain clothes and unadorned social presentation.
From what we know, Socrates stood out in both respects. His analytical method of definition inspired the philosophical tradition of examining and clarifying what we say and when, and it led to the development of logic. But as a human being he seems to have lived with integrity and steady virtue. (Famously, he did not escape execution despite having the opportunity to do so.) I think his unmatched status in philosophy has to do with this combination of personal magnetism and intellectual inventiveness and rigor.