If you increase your Sim's athletic skill, he or she might be offered the following opportunities.
Add it Up
After accepting this opportunity, increase your athletic skill by one level, and then return to the stadium.
At the Health Seminar
After accepting this opportunity, there will be an option to attend the health seminar at the hospital. This can only be performed between certain hours, so go into the map view and click on the hospital, then hover over the yellowish 'attend health seminar' interaction option to see what time of day you can perform this task. The health seminar lasts two hours.
Bursting with Energy
To complete this simple opportunity, all you need to do is work out until your Sim gains the Pumped moodlet. I don't know how long this takes, but it's easy enough to put your Sim on a treadmill and tell him or her to work out until fatigued, then keep an eye on his or her moodlets.
Desert Air... Good?
This opportunity requires the World Adventures expansion pack. Go to Al Simhara and jog for four hours, then go home.
The Complete Circuit
For this opportunity, you need to do work out with a TV OR stereo for 30 minutes, then go jogging for 30 minutes, then go swimming for 30 minutes. You don't have to do it all in a row. Just accumulate the minutes until the opportunity text box says that you completed all of them. It will say to go to the stadium to complete the opportunity when you have completed it.
A tracking device will automatically get added to your inventory. Make sure it's in your backpack. Then go jogging for one hour. The easiest way to ensure that you jog for an hour is to find a really far away spot and tell your Sim to jog there. Then when the hour is up, the opportunity text will reflect that and will tell you what to do next.
Work out with the Don't Break a Sweat option for three hours. The type of workout is up to you.