Colloquial contraction of 'to iu ka' used to rephrase or soften what was just said — 'or rather', 'I mean', 'how should I put it'.
彼、いい人だよ。ていうか、誰にでも優しいんだ。
He's a good person — or rather, he's kind to everyone.
今日は忙しい、ていうか手一杯で返事ができないよ。
I'm busy today — I mean, I'm swamped and can't reply.
あの店、安いっていうか品質が良くないんだよね。
That shop — or rather, it's cheap, but the quality isn't good.
Informally used like 'by the way' to change or add to the topic.
ていうか、今夜の食事はどうする？
By the way, what should we do about dinner tonight?
彼は来られない。ていうか、昨日急に熱が出てね。
He can't come — by the way, he suddenly had a fever yesterday.