1To hold in one's arms; to carry under one's arm; to cradle or hold something/someone.
母親は赤ちゃんを優しく抱えてあやしていた。
The mother gently held the baby and soothed it.
彼は重い箱を片手で抱えて運んだ。
He carried the heavy box tucked under one arm.
悲しいとき、彼女は枕を抱えて泣いた。
When sad, she hugged a pillow and cried.
2To have (problems, debts, responsibilities); to be burdened with something (e.g. debt, care of someone).
会社は多額の借金を抱えている。
The company is burdened with a large amount of debt.
彼は家庭の問題を抱えながら働いている。
He works while dealing with problems at home.
その町は高齢化という課題を抱えている。
The town faces the problem of an aging population.
3To employ; to have (on one's staff); to hire (people as part of an organization).
その会社は海外にも多くの社員を抱えている。
That company has many employees overseas as well.
小さな店だが、若いスタッフを数人抱えている。
It's a small shop, but it has a few young staff members.