To strive, I think, is to do everything in your power to accomplish something. If you strive for something, you have a desire to do it, you put all you effort into it, and you learn something in the process. Striving for something is honorable and noble, so long as what you strive for is wholesome and doesn't belittle or harm people on your path to obtaining it.
Striving is better than trying. For example, I'll try to finish my homework tonight, versus I'll strive to finish my homework tonight. Striving is more enthusiastic, more diligent, more efficient. Trying is more half-hearted, more unproductive, more indolent.
Strive to do good. Strive to be a better person. Strive to obtain and hold onto happiness.