その上（うえ） is a formal expression used in Japanese to indicate that something is ‘besides’, ‘in addition to’, or ‘furthermore’ in relation to the previous statement. It primarily comes at the beginning of sentences before reflecting back on and adding new information in regard to what has already been said.
The literal meaning can be thought of as ‘on top of that (B)’, where ‘that’ is the information that has already been mentioned.
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高橋（たかはし）さんはとても頭（あたま）がいい。その上（うえ）、人柄（ひとがら）もいいので会社（かいしゃ）での評判（ひょうばん）がいいです。
Takahashi-san is very smart. Furthermore, he has a very good personality so he has a very good reputation in the company.
今（いま）住（す）んでいる家（いえ）はものすごく小（ちい）さい。その上（うえ）隣（となり）に住（す）んでいる住人（じゅうにん）が一日（いちにち）中（じゅう）うるさいので、来月（らいげつ）引（ひ）っ越（こ）そうと思（おも）う。
The house I live in now is extremely small. In addition, the people who live next door are noisy all day long, so I'm thinking of moving out next month.
今日（きょう）は学校（がっこう）で先生（せんせい）に怒（おこ）られた。その上（うえ）家（いえ）に帰（かえ）ったら親（おや）に怒（おこ）られたのであまりいい一日（いちにち）ではなかった。
I was scolded by my teacher at school today. In addition, I was scolded by my parents when I came home, so it was not a very good day today.
Despite often being used in formal settings, it is not uncommon to hear this phrase used in daily speech, due to its simplicity in highlighting something being ‘in addition’.