The Japanese word for "balcony" is a loanword of veranda - ベランダ (Beranda). Veranda is a Anglo-Indian word from Hindi varanda which came from Portuguese varanda and is extensively used in India. So, Japanese took this word and katakanized it forming ベランダ. But, why there isn't there an actual Japanese word? Is it because long balcony or terrace is uncommon in Japanese architecture or any other reason?
2 Answers
Traditional Japanese houses are made of wood, so it was indeed fairly uncommon to have balconies above the first (ground) floor due to durability issues. However, some castles and temples did have one or more balcony-like structures, and such structures were called 縁側 (engawa) or simply 縁 (en) in non-katakana Japanese. Wraparound ones were also called 廻縁 (mawari-en). See this article (in Japanese) for details. 金閣寺 (aka 鹿苑寺) is an example of an old temple that had 縁側 on upper floors (picture):
鹿苑寺
二層は鎌倉時代の武家造りの建築様式で「潮音洞」とよばれ、四周に縁と高欄をめぐらし、外面と高欄を全面金箔張りとする。
However, as the linked Wikipedia article suggests, 縁(側) is a word that vaguely refers to narrow areas around tatami-matted rooms regardless of its height. Practically, most 縁側 are located slightly above the ground, so they are more like verandas or decks rather than Western balconies. So you may say Japanese had no good word that precisely corresponded to English "balcony".
Today, the word 縁側 is used only with traditional Japanese houses. When talking about western style houses, including apartment houses, we almost always use ベランダ/バルコニー (if it's on the second floor or above) or テラス (if it's on the first floor). Note that ベランダ in Japanese normally refers to structures located on the second floor or higher.
See also: Why is there ベッドルーム when there's already 寝室?
EDIT: This Wikipedia article on バルコニー mentions the word 露台, but according to this entry and actual examples on 青空文庫, this is a word that was used for a while in the 19th century as the translation of English balcony. This does not mean balcony-like structures in traditional Japanese buildings were called 露台.
Vocabulary in general: "Why does Language A have / not have a match for Word X in Language B?"
Adding onto naruto's answer, I'd like to point out that any word exists in any language in order to describe something relevant to speakers of that language. Simply put, Japanese architecture does not traditionally have "balconies". Since the thing did not exist, there was no need for a word to talk about it.
We could similarly ask why English does not have a native word for "tofu": put simply, soybeans were much less a staple of the English diet, and the very idea of boiling the proteins out of them and then creating curds from the resulting stew just never occurred to anyone in the English-speaking world. Likewise with the lack of any native word for "cheese" in Japanese. 😄
Architecture terms: What really is a "balcony" / "veranda" / "engawa"?
As a part of a building, a balcony is a platform sticking out from the face of the building, usually with a railing and usually above the ground floor. These may or may not have a roof (usually they don't, I think), and they are open to the elements. These are common features of Western buildings, but they are basically non-existent for traditional Japanese construction.
Technically speaking, a veranda is not a balcony either, but more of an outdoor porch along the side of a building, optionally screened in but generally open to the outdoor air. These are intended to be used as additional living space, not just as passageways, and tend to be wide and roomy.
Japanese architecture does have the 縁側【えんがわ】, as naruto notes. An engawa is also not a balcony, as we can tell by looking at the linked Wikipedia article and the pictures: an engawa is more like a hallway than a solitary platform, a long and skinny passage running along the outer edge of a building, traditionally enclosed with wooden and/or glass sliding doors on the outside, and shoji or rice-paper sliding doors on the inside. These are not outdoor living rooms, and are much less roomy than verandas.
Terminology
Ultimately, we have three distinct things, with three distinct names — in both English and Japanese.
So in answer to your original question, "Why isn't there an actual Japanese word for 'balcony'?", the simple answer is "because there weren't any actual balconies in the Japanese-speaking world."