泣きそうだ とはどういう意味ですか?

質問を翻訳

泣き - it's crying; to cry. right?
but what is it with "そうだ "?
a situation, from where that has taken:
1 person is embarrassed and keeps the second person by the edge of clothes.
the second does not look at him, does not express emotions.
but both of them think those "泣きそうだ".
The meaning of the text refers to love.

Thanks for any help!