(an expression of) understanding and care for someone else's suffering

The president has sent a message of sympathy to the relatives of the dead soldiers. 总统已经向阵亡士兵的家属发去了唁电。

I don't have much sympathy for her - I think she's brought her troubles on herself. 我不太同情她——我觉得她是在自找麻烦。

to express your sadness to someone because a relation or friend of theirs has recently died

I went along to the funeral in order to offer my sympathies. 我去参加了葬礼以表吊慰。

support and agreement

I must confess I have some sympathy with his views. 我必须承认我比较赞同他的观点。

support

Of those people questioned, 93 percent said their sympathies were with the teachers. 接受调查的人当中有93%表示支持教师。

He is known to have right-wing sympathies. 大家都知道他支持右翼。

to stop working in order to show your support for other workers who are on strike

The railway workers came out in sympathy with the miners. 铁路工人加入了罢工，声援煤矿工人。