The difference between a positive externality and a negative externality is that the former has good effects on people while the latter has bad effects.
An externality occurs when an economic action takes place and has an effect on people who are not directly part of the action. When an economic action takes place and other people are helped, it is a positive externality. When other people are harmed by the economic action, it is a negative externality.
Let us look at an example of each of these. For example, let us imagine that a landowner a half mile from my house decides to build a casino on their land. I am not part of this economic action. However, the action has an impact on me. All of a sudden, there is a huge increase in traffic on my street at all hours of the day and night. My quality of life is decreased. This is an example of a negative externality. Now let us imagine that this landowner makes a very large park instead of a casino. Now, my kids can bike to the park and play. There are more places to take walks. I have gotten a benefit from something that I did not pay for. This is a positive externality.
Externalities are impacts of economic actions that affect people who were not directly involved with those economic actions. The difference between the two kinds that you mention is that negative externalities harm people while positive externalities are beneficial to them. To see how this could be the case, let us look at an example of each type.
Negative externalities are much easier to imagine than positive ones. The classic example of a negative externality is pollution. Imagine that there is a large factory upwind of your home. The factory is engaged in economic activity and you are not connected to that factory. The economic activity at the factory creates pollution and the pollution drifts downwind and settles on and around your home. It might make it hard for you to breathe. It might make your house dirty. In other words, it hurts you. This is a negative externality.
Education is an example of an economic activity that has positive externalities. If children in your town are educated, it helps everyone, even those who do not have children and are not part of the school system. Educated children are less likely to grow up and commit crimes. They will become better workers and might boost the economy of your town. Everyone benefits from this even if they are not involved in educating the children.
Thus, externalities occur when an economic activity impacts people who are not involved in that activity.