しかも is a conjunction in Japanese which is commonly translated as either ‘furthermore’, or ‘moreover’. This is a somewhat formal grammar pattern which indicates that both (A) and (B) exist at the same time, or are in unison.
しかも itself focuses on the overall topic, so will be used for giving objective opinions, such as observable facts, rather than personal opinions.
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しかも is a conjunction, it may be used between two phrases, or sometimes at the beginning of a second sentence, when referring back to the first.
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このテレビは画質（がしつ）がめちゃくちゃいい。しかも、受信機（じゅしんき）がついていないから受信料（じゅしんりょう）を払（はら）わなくてもいい。
This TV has a very good resolution, and what’s more, it doesn’t have a receiver, so you don’t have to pay a TV reception fee.
彼女（かのじょ）はとても頭（あたま）がいいし性格（せいかく）もいい。しかも、美人（びじん）だからもてないわけがない。
She is very smart and has a great personality. Moreover, she is beautiful, so there is no way that she is not popular.
あの店（みせ）は古（ふる）いし汚（きたな）い。しかも品揃（しなぞろ）えもよくないから、そのうち潰（つぶ）れるだろう。
That store is old and dirty. Moreover, they don’t have a good selection of goods, so they will probably go out of business soon.
Often, (A) will be considered the ‘base’ information, while (B) is extra information added on top of (A), or further explaining (A).
Fun-fact - Originally, しかも came from the combination of the archaic interjection 然（しか） ‘as such’, or ‘like that’, and the particle も ‘too’, or ‘also. In this way, some reflection can be seen between it and modern English phrases like ‘additionally’, where the (B) information is simply adding on to what is already known about (A).
Fun-fact - In modern writing, しかも may also appear as either 而（しか）も or 併（しか）も, although both are quite rare.