I wouldn't call it a seaside resort. If you are looking for a summer holiday destination, there are far nicer places to go. However, for a day trip, there are many nice attractions to suite every person whether it be raining or nice and sunny.
Southsea is located on the south of Portsea Island. It looks out towards the isle of wight. The stretch of water separating the isle of wight and Portsmouth is known as the solent and it is one of the busiest shipping lanes in the world per square mile. It offers passage for the car ferry to france, the ferries to the isle of wight and the navy as well as recreational craft, due to this, the water is not particularly clean. This mixed with the fact the beach has no sand on it makes Southsea a rather uninspiring prospect for a day on the beach.
However, Southsea has many other attractions including the D-Day museum which celebrates the actions of the heroic soldiers on June 6th 1944.
Southsea also has a small attraction park with a small roller coaster and other rides such as the log flume. these are nothing in comparison to places like Thorpe park or even Blackpool however they please the children!
Furthermore, southsea has a large common a stones throw from the beach which is excellent for kite flying and football. It is the site of many events such as the annual visit of the circus and the kite festival. It also offers a great place to play football and have fun. There are also a number of parks along the common which are all suitable for young children.
Southsea also has a pitch and putt and some very nice cafes and restaurants.
If you get bored, you can always jump on the hovercraft which is one of only two passenger hovercrafts in the world and go and explore the Isle of Wight.
Portsmouth is steeped in naval heritage, there are also some very interesting naval attractions nearby such as HMS Victory (lord Nelson's flagship from the battle of Trafalgar), HMS warrior, the first iron warship and many other monuments of great interest.

Overall, a great day out but not a good holiday destination.