A signing bonus, as the name suggests, is an upfront payment a player receives to sign his contract.
When it comes to salary cap accounting rules, signing bonuses and P5 salaries are completely different. The amount a player gets to sign can be prorated or spread across the life of the contract (up to a maximum of five years). Without proration, it would be extremely difficult for any team to pay the huge signing bonuses we’ve seen in recent years— Joe Flacco ($40 Million), Drew Brees ($37 M), Aaron Rodgers ($33.25 M) and Andrew Luck ($32 M).
Since this money has already been paid, a team is liable for all money owed to the cap even in the event it releases a player (who has prorated bonus money left in future years) (for dead money and acceleration, click here).
There are far more subtleties of the signing bonus (i.e. treatment of voidable years, etc.), as well as payments that are treated like a signing bonus (i.e. Option Bonuses and fully guaranteed Roster Bonuses).
Example: Joe Flacco, Baltimore Ravens
Flacco’s 2016 contract contained the largest signing bonus in league history, when he received $40 million for the stroke of a pen. This bonus carries a cap charge of $8 million in each of first the five years of his contract.
(NFL CBA, p. 92-95)