What did socrates hope to achieve by practicing the socratic method

He wanted to discover adequate definitions that would give knowledge of the essential nature of things

The Socratic method is a way to seek truths by your own lights.
It is a system, a spirit, a method, a type of philosophical inquiry an intellectual technique, all rolled into one.
Socrates himself never spelled out a "method." However, the Socratic method is named after him because Socrates, more than any other before or since, models for us philosophy practiced - philosophy as deed, as way of living, as something that any of us can do. It is an open system of philosophical inquiry that allows one to interrogate from many vantage points.
Gregory Vlastos, a Socrates scholar and professor of philosophy at Princeton, described Socrates’ method of inquiry as "among the greatest achievements of humanity." Why? Because, he says, it makes philosophical inquiry "a common human enterprise, open to every man." Instead of requiring allegiance to a specific philosophical viewpoint or analytic technique or specialized vocabulary, the Socratic method "calls for common sense and common speech." And this, he says, "is as it should be, for how man should live is every man’s business."
I think, however, that the Socratic method goes beyond Vlastos’ description. It does not merely call for common sense but examines what common sense is. The Socratic method asks: Does the common sense of our day offer us the greatest potential for self-understanding and human excellence? Or is the prevailing common sense in fact a roadblock to realizing this potential?
Vlastos goes on to say that Socratic inquiry is by no means simple, and "calls not only for the highest degree of mental alertness of which anyone is capable" but also for "moral qualities of a high order: sincerity, humility, courage." Such qualities "protect against the possibility" that Socratic dialogue, no matter how rigorous, "would merely grind out . . . wild conclusions with irresponsible premises." I agree, though I would replace the quality of sincerity with honesty, since one can hold a conviction sincerely without examining it, while honesty would require that one subject one’s convictions to frequent scrutiny.