I've been trying to find the translation for Te Aroha....and looking at the Maori online dictionary I found this....
aroha1. (verb) (-tia,-ina) to love, feel pity, feel concern for, feel compassion, empathise.
Aroha ana ngā tangi a ō mātou wāhine (HM 4/2009:1). / The crying of our women was heart-rending.
2. (noun) affection, sympathy, charity, compassion, love, empathy.
Tērā tātau e rongo kei te tuwha haere a Henare i ana hipi, i ana kau ki a Ngāti Porou, hei kaihaukai māna ki tōna iwi, he nui nō tōna aroha! (TP 7/1900:8). / We have heard that, because of his charity, Henare is distributing his sheep and cows to Ngāti Porou as feasts for his people. See also aroha nui.
aroha mai(verb) sorry, I'm sorry, my apologies - a modern usage.
arohanui(noun) with deep affection - often used in signing off letters to friends. More correctly, it should be written as two words, aroha nui.Te is the equivalent of The.It is the name of the mountain, and also the town founded in the gold rush, about 1830.
edited to add- thanks to Susan Heather (see comments) I now know that Te Aroha is the Mountain of Love.