When you talk to Jauffre about "Spies", he'll tell you that the guards have seen strangers on the road for a few evenings now. He can't send the Blades off to check on it without weakening the security at Cloud Ruler Temple, but he can certainly send you. You should go talk to Captain Steffan at Cloud Ruler and Captain Burd in Bruma. Your objective is twofold: Jauffre wants the spies dead and he wants you to find out what they know.
Captain Steffan tells you that the strangers have been seen in the evenings near the Runestones at the foot of the mountain. Captain Burd tells you that no one has reported seeing strangers, although Jearl just returned from a trip.
There are a couple of ways that you can proceed with this. I kind of prefer the quick-n-dirty method: kill everything and let the Nine sort things out. It's quick and avoids any unnecessary questions (Burd figures that it's safter to not know what you've been up to). You can approach this either from the front or from the back.
From the front, make sure no one's looking and pick the lock on Jearl's house. She and her friend will turn into Mythic Dawn agents and try to bash your brains out. From there you can retrieve the necessary keys from their bodies, explore the basement, find Jearl's orders and take them back to Jauffre to wrap things up.
From the back, investigate the Runestones near dusk where you can observe the spies just kind of loitering about. If your stealth is pretty good, you can track the two back to Bruma Caverns and the basement of Jearl's house and let them detect you. At that point they'll morph into Mythic Dawn agents and you can open up a big ol' can of whupass on them. If your stealth is not so good, they'll detect you quickly and morph and you can open up that big ol' can, anyway. Retrieve the necessary keys from the body or bodies and head for Bruma Caverns. From there you go into the Basement of Jearl's house where you can retrieve Jearl's orders, then up into Jearl's house where you can dispose of the other spy, if necessary, and then report back to Jauffre to wrap things up.
If you're not the quick-n-dirty type, you'll need to ask around town. A few people have some clues that can help you put together a strong enough case where Burd can safely look the other way while you break in and deal with Jearl and her friend. Ease the synapses of Jorek the Outcast (one of the beggars) with a few golds and he'll remember seeing someone he's never seen before looking out of one of Jearl's windows when she wasn't there. Ongar the World-Weary (lives right across the street and is the first of your Thieves Guild fences) and Arnora (next door) can give you similar stories, which you can then take to Burd, who will authorize you to search the house.
Now you're back to the front-door approach, but you don't have to worry about someone seeing you this time. Just pick the lock, open up that big ol' can of whupass on Jearl and her friend, retrieve the keys, get the note from the basement and then take it back to Jauffre to wrap things up.
See why I prefer the quick-n-dirty approach. I get to the same point without having to worry about boosting dispositions and tracking people down.
When you report to Jauffre, he'll tell you to talk to Martin. Martin has apparently made some progress with the Mysterium Xarxes.