Illyrio's chests are six oaken chests with iron hasps belonging to Illyrio Mopatis. Illyrio brings them with him from Pentos when he travels by litter with Tyrion Lannister to rendezvous with Haldon Halfmaester and Ser Rolly Duckfield. Haldon is already expecting the chests, Illyrio hands them over to him.
There is some candied ginger in one of the chests. There is armour. Clothing as well, court clothes, for all of Griff’s party. Fine woollens, velvets and silken cloaks. Also child’s clothing, musty but well made.  The chests also contain purses of silver.  and suitable gifts for Queen Daenerys Targaryen. 
It is not known what else they contain. They are not too heavy as Duck is able to shift them easily on one shoulder.
A Dance with Dragons
Illyrio and Tyrion meet Haldon Halfmaester and Ser Rolly Duckfield, who take on supplies from Illyrio and the six oaken chests.  Before they depart Illyrio tells them that there is a gift for Young Griff in one of them, some candied ginger. 
When they halt for supper Tyrion questions Duck and Haldon as to the contents of the chests. He tells them that he thought they contained gold for the Golden Company but after seeing Duck hoist a chest onto one shoulder he realises that if it were full of coin it would he could never have lifted it so easily.
You have some chests for us?—Haldon Halfmaester, to Illyrio
Court clothes, for all our party. Fine woollens, velvets, silken cloaks. One does not come before a queen looking shabby…or empty handed. The magister has been kind enough to provide us with suitable gifts.. —Haldon Halfmaester, to Tyrion Lannister
Ride back to the Shy Maid and return with Lady Lemore and Ser Rolly. We'll need Illyrio's chests as well. All the coin, and the armor. —Griff's orders to Haldon