一方（いっぽう）で is a combination of the
noun 一方（いっぽう） 'one direction', and the
case marking particle で, in its nuance as 'at'. Together, they are used in a similar way to a
conjunction particle, carrying the meaning of 'on the other hand', 'at the same time', or 'while'.
一方（いっぽう）で may be used after the
attributive form of other words, or at the beginning of new phrases.
今日（きょう）は晴（は）れる一方（いっぽう）で、明日（あした）から2週間（しゅうかん）降（ふ）り続（つづ）ける。
While today will be sunny, it will continue to rain for 2 weeks starting tomorrow.
この猫（ねこ）は可愛（かわい）い一方（いっぽう）で、人（ひと）を噛（か）む癖（くせ）があるので気（き）をつけてください。
This cat is cute, but on the other hand, it has a habit of biting people, so please be careful.
田舎（いなか）の日中（にっちゅう）は静（しず）かな一方（いっぽう）で、夜（よる）には虫（むし）やカエルの鳴（な）き声（ごえ）が朝（あさ）まで聞（き）こえる。
The countryside is very quiet during the daytime, but on the other hand, you can hear the insects and the frogs from night through to morning.
彼（かれ）は歌手（かしゅ）である一方（いっぽう）で、政治家（せいじか）でもある。
He is a singer, while at the same time, a politician.
一方（いっぽう）で、長野県（ながのけん）では夏（なつ）祭（まつ）りが開催（かいさい）される。
On the other hand, the summer festival will be held in Nagano Prefecture. (The previous sentence would have had some contradictory information)
As
一方（いっぽう）で has a literal meaning similar to 'at the (A) side', or 'in the (A) direction', it is expressing that another direction also exists, which may then be compared or contrasted with (A).
Do not confuse
一方（いっぽう）で, with
一方（いっぽう）だ (or で in its conjunctive form). The expression that uses the で particle means 'at one direction/side', while the expression that utilizes the
auxiliary verb だ (or で in its conjunctive form) means 'in one direction'.
毎月（まいつき）お金（かね）が減（へ）っていく一方（いっぽう）で、全然（ぜんぜん）貯（た）まりそうもない。
Every month I keep losing money, and it doesn't even seem like it will increase.
私（わたし）のお金（かね）は貯（た）まっていく一方（いっぽう）で、彼（かれ）のお金（かね）は減（へ）っていくばかりです。
My savings is increasing, on the other hand, his savings continue to decline.
The overall context of the sentence will usually reveal whether the conjunctive form of だ (で) is being used, or the actual で particle.