An SLO is a measurable target — for example that 99.9 percent of requests over a month should succeed within a certain time — set from what users actually notice, not from what the technology can do. The target is measured with one or more SLIs (service level indicators), and the error budget is simply the distance between the target and one hundred percent: at 99.9 percent, roughly 43 minutes a month may go wrong.
The point is to turn the trade-off between speed and stability into a decision instead of an argument: while the budget holds, the team can deploy often and experiment; once it is spent, releases slow down until reliability is back. The concept comes from Google's SRE book and is the core of Site Reliability Engineering.