JR

JR, short for Japan Railways, is the primary railway operator in Japan and was owned by the government until the 1980's. It is now split up into a few different flavors based on region.

The JR sub-company that is active in most of Mie is JR Central (ＪＲ東海 JR Tōkai), with its official name being Central Japan Railway Company (東海旅客鉄道 tōkai ryokyaku tetsudō). JR Central is headquartered at Nagoya Station and runs the vast majority of the trains in Aichi, Mie, Gifu, and Shizuoka Prefectures (the Tōkai region). They also operate the Tōkaidō Shinkansen between Tokyo and Shin-Osaka -- Japan's most-travelled bullet train line.

JR West is active in a small part of Mie as well. The parts of the Kansai Main Line west of Kameyama Station (Seki, Tsuge, Iga, etc) are owned and operated by JR West.

Lines

Kansai Main Line (関西本線)

A line that connects Nagoya and Osaka. In Mie, it runs from Kuwana ~ Iga.

The Nagoya-Kameyama portion of this line is considered part of the Nagoya metro railway network and so trains run fairly frequently along this part. West of Kameyama trains run only once an hour and are notoriously slow. The line's name implies that it has great significance, however in reality it is a line with extremely low ridership (particularly west of Kameyama).

Kisei Main Line (紀勢本線)

A giant line that snakes all the way around the Kii Peninsula. The portion in Mie is from Kameyama ~ Kihō, it runs almost the entirely vertical length of the prefecture and is the only train service available in southern Mie.

The name is based on a kanji compound meaning the "Kii-Ise Line". It refers to the old province names, with Kii Province (紀伊) being modern-day Wakayama Prefecture and much of south Mie and Ise Province (伊勢) being what is today northern, central, and part of eastern Mie Prefecture.

Trains on this line are infrequent, maybe once an hour or less. The "Nanki Limited Express" runs down much of this line, connecting Nagoya and northern Mie to Owase, Kumano, Mihama, and across the border into Wakayama at Shingū and the onsen at Kii-Katsu'ura.

Sangū Line (参宮線)

This is the JR line that runs between Taki and Toba via Ise. It is as a branch line off the Kisei Line for the purpose of providing transport to Ise Grand Shrine.

Trains on this line are more frequent than along the Kisei Line south of Taki, and the "Mie Rapid" (to and from Nagoya) runs along this line.

Meishō Line (名松線)

A sad and tragic line that was never completed and, due to a typhoon in 2009, lost the final portion of its track. Due to low ridership, JR has no intention of repairing the track, and will instead run a bus between these stations now.

It was originally designed as a line to connect Nabari and Matsusaka (hence the 名 and 松 kanji in the name) to compete with Kintetsu but was only completed as far as Ise-Okitsu in Tsu.

Trains run very infrequently, maybe once every two hours.