For Prime Minister Netanyahu, the meeting symbolizes Israel's proactive commitment to the peace process. His talks with the president of Egypt are symbolic given the historic Israel-Egypt Camp David Accords of 1979. Additionally, Netanyahu's urging Mubarak to push the PA to direct talks is a not-so-subtle statement of blame for the failure of US-mediated peace talks which broke down late last year. Finally, given the 80-year-old Mubarak's ailing health, the meeting is intended to ensure a successful transition of peaceful relations with Israel after the death of the Egyptian leader.
For Prime Minister Mubarak, the meeting indicates that he is still a salient and relevant leader. It also highlights Egypt's central role as a broker of peace in the Middle East. Pressuring Netanyahu to reconsider his stance on settlements allows Mubarak to appease those who would berate him for "going soft on Israel" in his old age, while meeting with him allows him to maintain the stability of the peace agreement.
Overall, the meeting between the two leaders legitimized Israeli-Egyptian relations and allowed both leaders to strengthen their positions and that of their respective countries. What, if anything, lies ahead for the peace process remains to be seen.