1For an opening, passage, or wound to become closed or sealed off — e.g., a road being blocked, a wound healing shut. The kanji 塞 became jōyō in 2010, but this verb form is still commonly written in kana.
事故で高速道路の片側がふさがっている。
One side of the expressway is blocked due to an accident.
ようやく傷口がふさがってきた。
The wound has finally started to close up.
あいた口がふさがらないとはこのことだ。
This is exactly what they mean by 'left speechless' (lit. one's open mouth doesn't close).
倒れた木で山道がふさがれていた。
The mountain path was blocked by a fallen tree.
2For a pipe, drain, or opening to become clogged or plugged up so that something can no longer pass through — typical of noses, drains, filters, etc.
風邪で鼻がふさがって苦しい。
My nose is stuffed up from a cold and it's miserable.
排水口が髪の毛でふさがってしまった。
The drain got clogged with hair.
ホースの先が泥でふさがっている。
The end of the hose is clogged with mud.
3For a seat, room, schedule, or capacity to be occupied or taken — already in use and unavailable. Common in expressions like 会議室がふさがっている (the meeting room is occupied), 予定がふさがっている (my schedule is full), and 手がふさがっている (my hands are full).
申し訳ありませんが、その日はすでに予定がふさがっています。
I'm sorry, but my schedule is already booked that day.
今は手がふさがっているので、後でかけ直します。
My hands are full right now, so I'll call you back later.
週末のホテルは全部ふさがっていた。
All the hotels were fully booked for the weekend.
会議室は午後ずっとふさがっている。
The meeting room is occupied all afternoon.