A spring is a place where you can see water coming out of the ground. If it does this a lot, it will probably have washed any soil away, and so will be the start of a stream. If it only does it occasionally, it may well spring out through grass for a few days, as you can see in the picture above.
A spring is connected to the level of water in the soil and rocks below the surface. If the rock can allow water to flow through it, for example because it is a limestone or chalk, then in times of wet weather water will build up in the rock until it finds a way of getting out. The lowest places will be springs for much of the year, but in very wet weather, for example, winters, the lower springs may not be enough to let all of the water out, and so it will build up until it finds other places to come out. This gives the occasional springs.