What's the minimum amount of bandwidth for a website?
Let's say I have a hosting service with 125GB traffic, how many websites I can store before they start to slow down?
Also, what does "1000 Mbit uplink" mean? What is going to influence?
There is no minimum amount. A truly unpopular website will attract no traffic and require no bandwidth. Most site, will however fare a little better but it all depends on how much traffic the site gets.
125 GB per year? day? hour? second?
Per year, this isn't all that much.
Per day it would require at least 12.5 Mbits/sec just to be able to move the data assuming the demand was perfectly even.
Assuming you have a 1000 Mbit/second connection (i.e. you can shovel 1 gigabit - about 120 megabytes - per second) you could in theory host 80 such sites, but that would FULLY utilize your maximum theoretical bandwidth. In practice a 1 Gbit/sec link will never reach that theoretical maximum.
Worse yet, demand is far from even. So even if the aggregate amount of data transfered per day is 125 Gigabyte you may find that the load will vary from near zero to 100+ Mbits/sec! This depends on the type of site, but almost all sites but the most global ones will follow the daily rhythm of night and day. So your 1 Gbit/sec link would probably struggle to handle even just 20-40 sites that each require about 125 GiB of bandwidth per day during peak hours.
If the traffic is 125 GB per month per site (as comment indicates) than a 1 Gbit/sec link should be able to easily handle on the order of 1000 sites. This represents an average bandwidth requirement of under 0.5 Mbits/sec.