To speechify is to talk at people as if you were giving a formal speech, when nobody asked you to and when the moment does not call for it. The word is a small joke at the speaker's expense. It says: you are enjoying the sound of your own voice, you are performing importance, and we all have to stand here and wait. Picture an uncle at a family dinner who stands up with his glass and talks for eleven minutes about the meaning of family. That is speechifying. So it is not a neutral word for 'make a speech' — if your teacher gives a speech at graduation, you would never say she speechified unless you disliked it. The -ify ending is doing the mocking work here, the way it does in 'preachify' or the way we say someone is 'lecturing' us. It is a fairly rare, slightly old-fashioned, bookish word. You will meet it in newspapers and novels more than in daily conversation. British writers use it a bit more than American ones. It is also used as a noun-ish thing in the form 'speechifying' ('enough speechifying, let's eat'), which is honestly more common than the plain verb.

長篇大論、擺出演講架勢說教（帶嘲諷）。中文比較接近「發表偉論」「訓話」「講個沒完」。不要用「演講」來記，「演講」是中性的，speechify 一定帶白眼。