"Speak (talk) in riddles" means to express oneself in an ambiguous or puzzling manner.
When someone talks in riddles or speaks in riddles, they talk in a slightly strange, or mysterious way and it is not clear what they mean.
Bonus: "Enigma". An English word comes from a Greek word that means "to speak in riddles", and refers to something or someone that is mysterious, puzzling, or difficult to figure out.
Egypt's ancient pyramids and quantum mechanics, for example, might be described as enigmas, as well as physicist Stephen Hawking. In these uses, the word's meaning is a figurative extension of the original "riddle" sense. Many things have been named Enigma, including a rock band, a video game, a rollercoaster ride, and a very famous coding machine used in World War II.
- From multiple sources with editing
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I found an interesting poem by Edward Thomas (1878-1917), a British writer of English poetry and prose. It's about him observed a Thrush (画眉鸟) singing happily, without worrying about seasons like people often do.
But when I read it, I felt like he was speaking in riddles, especially with names of the months. Maybe it's the nature of a poet? 
Nevertheless, the poem was beautifully written, and yet, in very simple words. Below is my reading and the poem for fun and relaxation, when you have time 
“The Thrush”
- Edward Thomas
When Winter's ahead,
What can you read in November
That you read in April
When Winter's dead?
I hear the thrush, and I see
Him alone at the end of the lane
Near the bare poplar's tip,
Singing continuously.
Is it more that you know
Than that, even as in April,
So in November,
Winter is gone that must go?
Or is all your lore
Not to call November November,
And April April,
And Winter Winter—no more?
But I know the months all,
And their sweet names, April,
May and June and October,
As you call and call
I must remember
What died into April
And consider what will be born
Of a fair November;
And April I love for what
It was born of, and November
For what it will die in,
What they are and what they are not,
While you love what is kind,
What you can sing in
And love and forget in
All that's ahead and behind.
