Socrates famously declared his own ignorance, "I know that I know nothing." He also famously stated that an unexamined life is not worth living. In stating his own ignorance, Socrates was not saying that he knew nothing. He was stating that he would never suppose or assume that he, or anyone else, was completely correct about anything. Employing this methodology, Socrates encouraged others (and himself) to examine themselves and their ideas, no matter how certain they might be about a certain statement.
Socrates extended this principle to his use of what we call the Socratic method. This method is illustrated perhaps most famously in many of Plato's dialogues. Socrates was a huge influence on Plato and he was one of Plato's most common characters in his writing. In such a dialogue, Socrates would pretend to be more ignorant than he actually was. He would engage in a debate with another person. He would then ask questions to prompt his opponent to rethink his (the opponent's) position. In the end, Socrates, by pretending to be more ignorant (Socratic irony), and by asking the right questions, actually gets his listener/opponent to come to a new determination of truth. Not only does this illustrate the usefulness of the Socratic method; it also encourages the opponent/student to think for himself and reconsider his position. This function of the Socratic method is still useful today in education; sadly it not used or embraced in many political debates. The student does not benefit as much if the teacher simply gives the answer; the student exercises his/her thinking skills if the teacher prompts the student to deconstruct the debate him/herself.
Not to mention, the wider implication of the Socratic method (as it relates to the statement "I know that I know nothing") is that the teacher is also fallible and can learn new truths via a dialogue or debate; even with a student.
The Socratic method is a dialectical method. In a dialectical debate, there are two viewpoints. The goal in a dialectic is to start with two different or oppositional statements and progress toward a deeper truth; one or the other is more true, or a synthesis of the two reveals a deeper truth. This method of asking questions to provoke a person to think their way to a certain truth is also called maieutics.
It is debatable whether Socrates thought that humans would become completely "wise." But he did believe that everyone should embark on the path to wisdom. Using questions to get his listener to realize new truths, Socrates showed that his listener does in fact have the ability to pursue wisdom.
Socrates and Plato believed in Ideal Forms, abstract ideas and concepts which are absolutely true in their perfect forms. Plato supposed that we lose knowledge such as this upon being born. The path to wisdom involves learning things in our mortal lives but also a kind of remembering (anamnesis) these concepts. It is an odd concept in which remembering and learning are conflated. With respect to Socrates' method of questioning his listener, he is motivating his listener to do the inductive work of seeking wisdom and if such an Ideal Truth is the goal during the dialectic, the process is one of trying to conceive and/or "remember" an Ideal Form; the realm of Ideal Forms, in its perfection, could be said to be a "divine" realm.