Decrypted and then re-encrypt all requests to the internet at firewall level

I don't have strong skills about this matter but I am very curious about the following communication so may I ask:

One institution sent a message to all network users saying that "all requests to the internet which are encrypted will be decrypted and then re-encrypted at firewall level". So my questions are: is this possible?! And how?

Examples are given: Google, Facebook, LinkedIn, ... which use encrypted connection. And also examples that stay out of this mechanism: sites tagged in the "financial" category.

If the keys are only shared by my computer and the website, how can the requests be decrypted? The institution is big and has resources, but I cannot imagine the firewall breaking the keys in run time for all requests.

I see that there are companies selling "SSL Decryption and Inspection" services.

Can someone explain me how this work please?