It means "He/she doesn't feel well/good." or "He/she is sick." **physically**. It's often used together with 体が, such as 体の具合が悪い.
このところ体の具合が悪い。(I haven't been feeling well lately)
Other than that, you could say something is in poor condition, not working well or something is wrong with an object.
クラッチの具合が悪いです。(The clutch isn't working right.)
ドライヤーの具合が悪いのですが。(There's somthing wrong with the drier.)