They wanted a close flyby of Triton. Triton's orbit is at a large angle to the ecliptic plane, and Triton was below Neptune at the time of Voyager's flyby, so they needed a course change that pointed "down" from Neptune.
From the Voyager Neptune travel guide (large PDF), page 118-119 of the PDF (page number 107-108 indicated on the page):
However, Voyager 1 passed (slightly) the leading hemisphere of Saturn, and Voyager 2 will pass (slightly) the leading hemisphere of Neptune. In these two cases, the spacecraft slowed down and the planets speeded up.
Neptune is Voyager 2's last planet. There being no next planet to seek (Pluto is not reachable; refer to Figure 6-2), Voyager 2 is not limited to passing Neptune through any particular gravity-assist corridor, and can instead concentrate on Neptune's large moon, Triton. Triton is as interesting to many planetary scientists as Neptune is. Triton is large enough to have an atmosphere. Its surface temperature and pressure are close to the triple point of nitrogen, raising the possibility of nitrogen clouds, frozen nitrogen pools, and snow/ice on the surface. In 1980, Andrey Sergeyevsky discovered that there was indeed a way to pass closely by both Neptune and Triton, thereby maximizing the scientific return from each. The means was a final application of the gravity-deflection concept. The spacecraft would pass very close to Neptune (within 4850 kilometers of the cloud tops) in order to bend its path by about 45 degrees to pass close by Triton 5.2 hours later (see Figure 6-1.) The close passage of Neptune occurs near its North Pole, and is just barely on the leading hemisphere. Voyager 2 will slow down slightly (and Neptune will speed up even more slightly) as a result of this final gravity assist.
Image from Voyager mission status report 91, via Wikipedia
