Here is a fantastic, though somewhat outdated overview [1]. Section 5 is most relevant to your question. The network topology today is a little different. Think of Level3 as an NSP, which is now called a "Tier 1 network" [2]. The diagram should show links among the Tier 1 networks ("peering"), but does not.
tl;dr One of the large Internet backbone providers (formerly known as Level3, but now known as CenturyLink usually) that many ISPs use is down. Expect issues connecting to portions of the Internet.
Usually the Internet is a bit more resilient to these kinds of things, but there are complicating factors with this outage making it worse.
Expect it to mostly be resolved today. These things have happened a bit more frequently, but generally average up to a couple times a year historically.
[1] https://web.stanford.edu/class/msande91si/www-spr04/readings...
[2] https://en.wikipedia.org/wiki/Tier_1_network