From Reddit,
https://www.reddit.com/r/syriancivilwar/comments/4m3f8b/manbij_offensive_megathread/
Why is Manbij so important?
Manbij is the third largest city that IS controls in Syria, after Deir-Ezzor and Raqqa, thus it is an important population center and losing it would prove to be another blow to IS who have lost Palmyra to the Syrian Arab Army in March 2016. For the SDF and more specifically the YPG, linking the cantons is one of the main goals, this means connecting Al-Hasakah to Afrin in one stretch of land. This would greatly improve the position of the SDF at the negotiating table (despite not being invited during the Geneva III process) as they can try to claim autonomy from the captured territory, they are currently 70 km away.
What about IS? One of the main smuggling routes of IS (to my knowledge) is the Jarabulus route, most of the fighters that came from Belgium entered Syria through this checkpoint. Capturing Manbij would extend the supply lines for IS and force them to pass through Al-Bab or intermediary routes in order to get the the rest of IS territory in and Syria. However if Tabqa is taken IS will be closed off from its main smuggling route and isolated in Aleppo and would rely on captures from other belligerents.
How has the offensive been going?
Initially the situation looked like
this, before the offensive that was carried out. From the first of June to the third of June things have evolved heavily which can be seen in
this Gif. The SDF has steadily advanced the past three days and made solid advances in the area, as can be seen from the maps, the SDF uses plenty pincer movements in order to capture IS territory, this worked previously when the SAA emptied the area between Al-Safirah and Kweires airbase from IS fighters.
What are the next supposed plans?
There have been reports that the SDF is trying to attack Manbij from the south, west and north and that they have now planned to stop advancing on the southern axis to give time to the rest of the SDF components to arrive and position themselves to capture the city.
Leaflets dropped over Manbij,
Apparent translation,
isis fighter calling for reinforcement leader reply: i will send you 100 more, hold on your positions
man standing beside leader: but we have no more men, he told us the same lie 100 times before..