On-time payments is very straightforward but may be very difficult to manage in real life. It is simply a measure of what percentage of all of your credit payments was made all time. The ideal here, of course, is to get to 100%. If it's not 100%, then as close to 100% is ideal. This is one of the most important factors to credit score and is one of the most difficult to recover.
Although the key to good credit is simply to make a satisfactory payment (at least the minimum payent) on time, this is usually not enough for a healthy overall personal finance life, especially when it comes to credit cards. The actual details of the calulation may vary but generally the minimum payment comes to ~2-3% of your total balance or $25, whichever is lower. Because this explicitly leaves balance on the card, you will find yourself paying hefty interest charges if you only make the minimum payment.
This presents a similar problem when you look at mortgages: 30-year mortgages have much lower payment requirements than 15-year mortgages but they amortize slower and have higher interest rates. This means that the mortgage that is easier to maintain hitting the minimum payment on may be worse in total interest in the long run.
Credit histories last a long time, especially if you had a rough patch or missed a few payment. That payment you forgot 2 years ago or that short bout of unemployment that made you miss a few payments a couple months ago may feel like it's a long time ago but still impacting your ability for credit. This can be especially frustrating when it comes to finding great places to rent or even finding a job, so much so that it is easy to get discouraged and feel that the system sets it up so that it is harder to get ahead when you're already behind (just like credit card benefits flow to prime users and credit card interest flows to subprime users).
The key is simply a level head. So long as you continue to make on-time payments, the number will continue to increase. Similar to the AA mantra of "one day at a time", "one payment at a time" is the only way that you can improve this number consistently over the long haul. The good news is that companies look at the timing of the missed payments as well as the overall percentage. A 95% on-time payment rate where the missed payments are over three years ago will be looked more favorably upon than a 95% on-time payment rate where the missed payments were last month (maybe even better than a 97% where missed payments were last month!). As the actual missed payments age, they not only blend into a higher number of actual on-time payments but they also age in importance.
A missed payment in the past can sometimes best be treated with a shrug
One caveat to the on-time payment is what is known as a grace period. Grace periods are factored into a few contracts which allow small late payments to not be reported as late. Some other features sometimes include waiving any late fee that may come with it. These clauses are usually standard practice in mortgage, where a missed payment up to 15 days late will not be counted negatively from a credit OR late fee standpoint. This treatment is rarer for credit cards though, although many will waive a first-time late fee (although they may still report it as late AND waive the late fee!) for a long-term on-time customer. Your mileage may vary.