From the top:
the left-hand shield shows who is directing the siege (it might not be you, if your allies have sent an army commanded by a higher-ranked general than you have available) and who will take the province if the siege is successful. The right-hand shield shows the defenders, who currently control the province.
The two skulls show attrition rates: the important one is the one on the left. If this is bigger than 0, your army is losing that percentage of its troops each month. If it's red, your out of supply, which means you're losing even *more* troops each month.
The two numbers in circles are relative strength of the besieging and defending forces. When the right-hand circles reaches -10 the siege has been successful: it goes down more quickly if you have a commander with a siege value (eg. Cortez of Spain, Vauban of France) or lots of cannon. In the above example, the values are 0 - 3 which means the siege has a long way to go before being successful. If the left number is higher than the right, things are going well; but I must confess I don't understand exactly how they're worked out.
Hover over the picture of flaming buildings in the box, to see how many months the siege is expected to last. It can come down very quickly if you have sufficient cannon (30 per level of fortress, or 40 per level of fortress, are the important numbers here).
Strong-Strong are the relative morale levels. These are only relevant in the case of a fort being assaulted, and work in the same way as during a regular battle. If the besiegers break, the assault fails but the siege goes on. If the defenders break, the city falls immediately. Cavalry take no part in an assault, although they can besiege a city.
The numbers of troops on each side are self-evident; infantry, cavalry and cannon.
"Cover" means leave enough troops behind to cut the enemy's supply lines, but NOT enough to carry on the siege.
"Besiege" means leave enough troops behind to continue the siege, and let the rest move on somewhere else. Note that in both cases, you cannot choose which parts of your army remain behind. I don't know how the game engine decides for you.
"Assault" means launch an attack on the fortress: if you have a sufficiently large and high-morale force, and/or good generals, this can win the fortress very quickly, but if you don't, it can wipe out large chunks of your army for no benefit.
Hope that helps.