A man who wants to marry a particular woman, and who is openly trying to win her — visiting her, courting her, asking her family. The word carries its own century with it: it belongs to a world where marrying was a public, arranged, competitive business, so you meet it in Jane Austen, in fairy tales, in history books, in a princess's court where several suitors compete. Nobody today says 'my suitor' about a boyfriend without joking. When modern speakers do use it straight, it is usually with a wink — 'she had no shortage of suitors' — a slightly grand, amused way of saying admirers. There is a second, very much alive sense that has nothing to do with romance: in business news, a suitor is a company that wants to buy another company. 'The board rejected the German suitor' means a German firm tried to buy them and was turned down. That sense is entirely normal in today's newspapers, and it is honestly the one a student is more likely to meet in real English. Note that the old sense is one-directional: traditionally the man is the suitor and the woman is the one courted, which is part of why the word feels dated.