According to what you explained, its apparent that you have a cheap stereo system. You can buy better speakers, however they should be of the same wattage and ohm rating if its indicated on the back of the system. Otherwise you are taking a chance of damaging the stereo or the new speakers that do not meet similar specifications. You will hear a noticable difference however its anyone's guess as to how long it will be before the system dies. It may very well work great for the next 10 years. But being that its a cheap system its well worth taking a chance.

The RCA jacks might be intended for speakers or they may be a line-level output for an external amplifier and speakers or for powered speakers. Only your manual will tell you for sure. If you are unsatisfied with the audio quality of your system, you may not find much of an improvement with the available options. Better-quality speakers can be used in place of the existing ones. However, if the system upstream is not very good, you will experience only a marginal improvement. In my opinion, the most important component in any system is the signal source (e.g., CD / SACD / DVD-A player, turntable, tuner). Most people disagree with this viewpoint and feel that the speakers are the most important. A poor-quality source can be connected to the best amplifier and speakers in town, but the system will only sound as good as the source allows. The sources included in budget systems are usually not that good. The mass-market audio industry has, for years, been producing source components of lower and lower quality. More resources seem to be directed towards appearance, in place of sound quality. I would recommend that you replace the unsatisfactory system with one with a better-quality source. If you are looking for the cheapest solution, you may not find yourself with many options. However, with a great deal of care, a fine audio system (CD, integrated amplifier, speakers) can be assembled for under US$1000. Before you gasp in shock at this number, think about it: many people have no trouble dropping thousands on a TV, but gag when confronted with a $200 price tag for an audio system. You do tend to get what you pay for.